{"id":21088,"date":"2026-01-10T13:58:33","date_gmt":"2026-01-10T05:58:33","guid":{"rendered":"https:\/\/3d-universal.com\/en\/?p=21088"},"modified":"2026-01-10T14:02:27","modified_gmt":"2026-01-10T06:02:27","slug":"measurement-and-units","status":"publish","type":"post","link":"https:\/\/3d-universal.com\/en\/blogs\/measurement-and-units.html","title":{"rendered":"Measurement and Units: NMAT Physics Review"},"content":{"rendered":"<p><!--more--><\/p>\n<h1>Measurement and Units: NMAT Physics Review<\/h1>\n<h2>Why Measurement Matters in NMAT Physics<\/h2>\n<p>Physics is built on measurement. Every law, formula, graph, and experiment depends on describing the real world with numbers and units. In the NMAT, many \u201chard-looking\u201d problems become simple once you handle units correctly. If you can convert units quickly, identify the right base quantities, and apply dimensional analysis, you can solve questions faster and avoid common traps.<\/p>\n<p>This review focuses on the essential ideas you need: the SI system, prefixes, unit conversion strategies, dimensional analysis, significant figures, and common measurement instruments. You\u2019ll also learn practical exam shortcuts that help you check answers without doing long computations.<\/p>\n<h2>Physical Quantities: Base vs Derived<\/h2>\n<p>A physical quantity is something measurable with a magnitude and a unit. In physics, quantities fall into two main types:<\/p>\n<ul>\n<li><strong>Base (fundamental) quantities<\/strong>: defined independently and form the foundation of the unit system.<\/li>\n<li><strong>Derived quantities<\/strong>: defined using base quantities through relationships (like speed = distance\/time).<\/li>\n<\/ul>\n<p><strong>SI Base Quantities and Units<\/strong><\/p>\n<ul>\n<li>Length \u2014 meter (m)<\/li>\n<li>Mass \u2014 kilogram (kg)<\/li>\n<li>Time \u2014 second (s)<\/li>\n<li>Electric current \u2014 ampere (A)<\/li>\n<li>Temperature \u2014 kelvin (K)<\/li>\n<li>Amount of substance \u2014 mole (mol)<\/li>\n<li>Luminous intensity \u2014 candela (cd)<\/li>\n<\/ul>\n<p>Most NMAT questions use the first three heavily (m, kg, s), plus derived units such as Newtons, Joules, and Pascals. You should be able to express any derived unit in terms of base units when needed.<\/p>\n<h2>SI Derived Units You Must Know<\/h2>\n<p>Derived units combine base units. Here are the most important ones for NMAT-level physics:<\/p>\n<ul>\n<li><strong>Area<\/strong>: m<sup>2<\/sup><\/li>\n<li><strong>Volume<\/strong>: m<sup>3<\/sup><\/li>\n<li><strong>Speed\/Velocity<\/strong>: m\/s<\/li>\n<li><strong>Acceleration<\/strong>: m\/s<sup>2<\/sup><\/li>\n<li><strong>Force (Newton, N)<\/strong>: kg\u00b7m\/s<sup>2<\/sup><\/li>\n<li><strong>Work\/Energy (Joule, J)<\/strong>: N\u00b7m = kg\u00b7m<sup>2<\/sup>\/s<sup>2<\/sup><\/li>\n<li><strong>Power (Watt, W)<\/strong>: J\/s = kg\u00b7m<sup>2<\/sup>\/s<sup>3<\/sup><\/li>\n<li><strong>Pressure (Pascal, Pa)<\/strong>: N\/m<sup>2<\/sup> = kg\/(m\u00b7s<sup>2<\/sup>)<\/li>\n<li><strong>Density<\/strong>: kg\/m<sup>3<\/sup><\/li>\n<li><strong>Charge (Coulomb, C)<\/strong>: A\u00b7s<\/li>\n<li><strong>Voltage (Volt, V)<\/strong>: J\/C = kg\u00b7m<sup>2<\/sup>\/(s<sup>3<\/sup>\u00b7A)<\/li>\n<li><strong>Resistance (Ohm, \u03a9)<\/strong>: V\/A<\/li>\n<\/ul>\n<p>Even if you don\u2019t memorize every derived unit, you should memorize at least Newton, Joule, and Pascal in base-unit form. These show up often in dimensional analysis and unit-check questions.<\/p>\n<h2>Metric Prefixes and Powers of Ten<\/h2>\n<p>NMAT physics often tests comfort with scientific notation and metric prefixes. Learn these common prefixes:<\/p>\n<ul>\n<li>Giga (G) = 10<sup>9<\/sup><\/li>\n<li>Mega (M) = 10<sup>6<\/sup><\/li>\n<li>Kilo (k) = 10<sup>3<\/sup><\/li>\n<li>Deci (d) = 10<sup>-1<\/sup><\/li>\n<li>Centi (c) = 10<sup>-2<\/sup><\/li>\n<li>Milli (m) = 10<sup>-3<\/sup><\/li>\n<li>Micro (\u03bc) = 10<sup>-6<\/sup><\/li>\n<li>Nano (n) = 10<sup>-9<\/sup><\/li>\n<\/ul>\n<p><strong>Fast mental rule:<\/strong> moving from kilo \u2192 base \u2192 milli is a 10<sup>6<\/sup> change (because 10<sup>3<\/sup> to 10<sup>-3<\/sup>).<\/p>\n<p>Also remember: the symbol \u201cm\u201d can mean <strong>meter<\/strong> (unit) or <strong>milli-<\/strong> (prefix). Context matters. \u201cmm\u201d is millimeter; \u201cm\u201d alone is meter.<\/p>\n<h2>Unit Conversion: The Factor-Label Method<\/h2>\n<p>The safest conversion strategy is the factor-label (dimensional) method. You multiply by conversion factors written as fractions equal to 1.<\/p>\n<p><strong>Example 1: Convert 72 km\/h to m\/s<\/strong><\/p>\n<ul>\n<li>Use 1 km = 1000 m<\/li>\n<li>Use 1 h = 3600 s<\/li>\n<\/ul>\n<p>72 km\/h \u00d7 (1000 m \/ 1 km) \u00d7 (1 h \/ 3600 s) = 72 \u00d7 1000 \/ 3600 m\/s = 20 m\/s<\/p>\n<p><strong>Example 2: Convert 2500 cm<sup>3<\/sup> to m<sup>3<\/sup><\/strong><\/p>\n<p>First convert cm to m: 1 cm = 10<sup>-2<\/sup> m. For volume, cube the factor:<\/p>\n<p>1 cm<sup>3<\/sup> = (10<sup>-2<\/sup> m)<sup>3<\/sup> = 10<sup>-6<\/sup> m<sup>3<\/sup><\/p>\n<p>So 2500 cm<sup>3<\/sup> = 2500 \u00d7 10<sup>-6<\/sup> m<sup>3<\/sup> = 2.5 \u00d7 10<sup>-3<\/sup> m<sup>3<\/sup><\/p>\n<p><strong>Key NMAT trap:<\/strong> when converting squared or cubed units, students forget to square\/cube the conversion factor.<\/p>\n<h2>Dimensional Analysis: Your Shortcut for Checking Formulas<\/h2>\n<p>Dimensional analysis checks whether an equation makes sense by comparing dimensions (not units). The dimension symbols commonly used are:<\/p>\n<ul>\n<li>[L] for length<\/li>\n<li>[M] for mass<\/li>\n<li>[T] for time<\/li>\n<\/ul>\n<p>A valid physical equation must be dimensionally consistent: both sides must have the same dimensions.<\/p>\n<p><strong>Example: Is v = at dimensionally correct?<\/strong><\/p>\n<ul>\n<li>Velocity v has dimensions [L][T]<sup>-1<\/sup><\/li>\n<li>Acceleration a has [L][T]<sup>-2<\/sup><\/li>\n<li>Multiply by time t ([T]): a\u00b7t = [L][T]<sup>-2<\/sup>\u00b7[T] = [L][T]<sup>-1<\/sup><\/li>\n<\/ul>\n<p>So v = at is dimensionally consistent.<\/p>\n<p><strong>Example: Deriving a relationship quickly<\/strong><\/p>\n<p>Suppose you forget the formula for period T of a pendulum but recall it depends on length L and gravitational acceleration g.<br \/>\nAssume T \u221d L<sup>a<\/sup> g<sup>b<\/sup>.<\/p>\n<ul>\n<li>[T] = [L]<sup>a<\/sup> ([L][T]<sup>-2<\/sup>)<sup>b<\/sup> = [L]<sup>a+b<\/sup>[T]<sup>-2b<\/sup><\/li>\n<li>Match powers: -2b = 1 \u21d2 b = -1\/2<\/li>\n<li>a + b = 0 \u21d2 a = 1\/2<\/li>\n<\/ul>\n<p>So T \u221d \u221a(L\/g). This technique is powerful for NMAT conceptual questions.<\/p>\n<h2>Scientific Notation and Estimation Skills<\/h2>\n<p>NMAT exams reward speed. Scientific notation helps you multiply and divide large\/small numbers quickly while tracking significant digits.<\/p>\n<p><strong>Rules to remember<\/strong><\/p>\n<ul>\n<li>(a \u00d7 10<sup>m<\/sup>) (b \u00d7 10<sup>n<\/sup>) = (ab) \u00d7 10<sup>m+n<\/sup><\/li>\n<li>(a \u00d7 10<sup>m<\/sup>) \/ (b \u00d7 10<sup>n<\/sup>) = (a\/b) \u00d7 10<sup>m-n<\/sup><\/li>\n<li>Keep the coefficient between 1 and 10 in final standard form.<\/li>\n<\/ul>\n<p><strong>Quick estimation tip:<\/strong> Round numbers to 1\u20132 significant digits before computing. Many multiple-choice options are separated enough that an estimate is sufficient.<\/p>\n<p><strong>Example: Estimate (3.2 \u00d7 10<sup>5<\/sup>)(4.8 \u00d7 10<sup>-3<\/sup>)<\/strong><\/p>\n<p>\u2248 (3 \u00d7 5) \u00d7 10<sup>5-3<\/sup> = 15 \u00d7 10<sup>2<\/sup> = 1.5 \u00d7 10<sup>3<\/sup><\/p>\n<h2>Accuracy vs Precision and Types of Error<\/h2>\n<p>These terms often appear in NMAT conceptual questions:<\/p>\n<ul>\n<li><strong>Accuracy<\/strong>: how close a measurement is to the true value.<\/li>\n<li><strong>Precision<\/strong>: how consistent repeated measurements are with each other.<\/li>\n<\/ul>\n<p>You can be precise but not accurate (tight clustering around the wrong value) or accurate but not precise (average is close but values scatter).<\/p>\n<p><strong>Common sources of error<\/strong><\/p>\n<ul>\n<li><strong>Systematic error<\/strong>: consistent bias (e.g., miscalibrated instrument). Affects accuracy.<\/li>\n<li><strong>Random error<\/strong>: unpredictable fluctuations (e.g., reaction time). Affects precision.<\/li>\n<li><strong>Zero error<\/strong>: instrument does not read zero when it should (common in vernier calipers and micrometers).<\/li>\n<li><strong>Parallax error<\/strong>: reading a scale from an angle instead of straight-on.<\/li>\n<\/ul>\n<h2>Significant Figures and Rounding Rules<\/h2>\n<p>Significant figures communicate measurement certainty. In NMAT problems, you may need to round final answers correctly.<\/p>\n<p><strong>Counting significant figures<\/strong><\/p>\n<ul>\n<li>Non-zero digits are significant (123 has 3 s.f.).<\/li>\n<li>Zeros between non-zero digits are significant (1002 has 4 s.f.).<\/li>\n<li>Leading zeros are not significant (0.0032 has 2 s.f.).<\/li>\n<li>Trailing zeros are significant only if a decimal point is shown (2.500 has 4 s.f.; 2500 is ambiguous without notation).<\/li>\n<\/ul>\n<p><strong>Rules in calculations<\/strong><\/p>\n<ul>\n<li><strong>Multiplication\/division<\/strong>: final answer has the same number of significant figures as the factor with the fewest s.f.<\/li>\n<li><strong>Addition\/subtraction<\/strong>: final answer has the same number of decimal places as the term with the fewest decimal places.<\/li>\n<\/ul>\n<p><strong>Example (Multiplication):<\/strong> (2.3)(4.56) = 10.488 \u2192 2 s.f. \u2192 10<\/p>\n<p><strong>Example (Addition):<\/strong> 12.11 + 0.3 = 12.41 \u2192 1 decimal place \u2192 12.4<\/p>\n<h2>Common Measurements and Instruments<\/h2>\n<p>NMAT physics may include basic instrument questions. Know what each instrument measures and typical precision.<\/p>\n<ul>\n<li><strong>Meter stick \/ ruler<\/strong>: length; least count often 1 mm (0.1 cm).<\/li>\n<li><strong>Vernier caliper<\/strong>: more precise length\/diameter; least count depends on vernier scale (often 0.01 cm or 0.02 mm depending on type).<\/li>\n<li><strong>Micrometer screw gauge<\/strong>: very small thickness\/diameter; can measure to 0.01 mm (varies by instrument).<\/li>\n<li><strong>Stopwatch<\/strong>: time measurement; human reaction time can introduce random error.<\/li>\n<li><strong>Triple-beam balance \/ digital balance<\/strong>: mass measurement.<\/li>\n<li><strong>Graduated cylinder<\/strong>: volume measurement; better than beaker for accuracy.<\/li>\n<li><strong>Thermometer<\/strong>: temperature measurement; note scale (\u00b0C vs K).<\/li>\n<\/ul>\n<p>For many NMAT problems, you won\u2019t need the instrument\u2019s exact least count, but you should know the idea: a smaller least count means higher resolution (more precision).<\/p>\n<h2>Temperature Scales and Conversion<\/h2>\n<p>Temperature commonly appears in physics and chemistry overlaps. The NMAT may ask about Celsius and Kelvin.<\/p>\n<ul>\n<li>Kelvin is the SI unit for temperature.<\/li>\n<li>Conversion: <strong>T(K) = T(\u00b0C) + 273.15<\/strong> (often approximated as +273)<\/li>\n<\/ul>\n<p><strong>Example:<\/strong> 27\u00b0C = 27 + 273 = 300 K (approx.)<\/p>\n<p>Be careful: temperature differences in Celsius and Kelvin have the same numerical value (a change of 1\u00b0C equals a change of 1 K), but absolute values differ by 273.<\/p>\n<h2>Density, Specific Gravity, and Unit Awareness<\/h2>\n<p>Density is mass per unit volume: <strong>\u03c1 = m\/V<\/strong>. The SI unit is kg\/m<sup>3<\/sup>, but g\/cm<sup>3<\/sup> is commonly used in lab-style contexts.<\/p>\n<p><strong>Useful conversion:<\/strong><\/p>\n<ul>\n<li>1 g\/cm<sup>3<\/sup> = 1000 kg\/m<sup>3<\/sup><\/li>\n<\/ul>\n<p>Specific gravity is the ratio of a substance\u2019s density to the density of water (at a reference condition). It has <strong>no units<\/strong> because it\u2019s a ratio.<\/p>\n<h2>Exam Tactics: Unit-Based Shortcuts<\/h2>\n<p>Here are fast, high-value tactics for NMAT multiple-choice problems:<\/p>\n<ul>\n<li><strong>Check units early<\/strong>: If an answer choice has the wrong unit, eliminate it immediately.<\/li>\n<li><strong>Use dimensional reasoning<\/strong>: If the question asks for energy, your expression must reduce to kg\u00b7m<sup>2<\/sup>\/s<sup>2<\/sup>.<\/li>\n<li><strong>Convert only when needed<\/strong>: Sometimes you can keep everything in cm and g as long as you stay consistent, then convert at the end (if required).<\/li>\n<li><strong>Watch squared\/cubed conversions<\/strong>: This is one of the most common error sources.<\/li>\n<li><strong>Estimate first<\/strong>: If your computed result is 10\u00d7 bigger than all options, you likely made a power-of-ten mistake.<\/li>\n<li><strong>Use \u201cunit cancellation\u201d<\/strong>: Write conversions so units cancel neatly; it prevents inverted factors.<\/li>\n<\/ul>\n<h2>Mini Practice Set (Concept-Focused)<\/h2>\n<p>Use these as quick self-checks. Try answering without a calculator, focusing on units and powers of ten.<\/p>\n<ol>\n<li>Convert 5.0 m\/s to km\/h. (Hint: multiply by 3.6)<\/li>\n<li>Express 1 N in base units.<\/li>\n<li>If pressure is measured in Pa, what are the base units of Pa?<\/li>\n<li>Which is larger: 0.45 mm or 4.5 \u00d7 10<sup>-5<\/sup> m?<\/li>\n<li>A cube has side 2 cm. What is its volume in m<sup>3<\/sup>?<\/li>\n<\/ol>\n<p>If you can do these quickly, you\u2019re in strong shape for measurement and units questions.<\/p>\n<h2>Summary: What to Master for NMAT<\/h2>\n<p>To score well on NMAT Physics measurement questions, you should be able to:<\/p>\n<ul>\n<li>Recognize SI base units and common derived units (N, J, Pa).<\/li>\n<li>Use metric prefixes confidently and move between powers of ten.<\/li>\n<li>Convert units using factor-label method (including squared\/cubed units).<\/li>\n<li>Apply dimensional analysis to check or infer formulas.<\/li>\n<li>Handle scientific notation and quick estimation.<\/li>\n<li>Understand accuracy vs precision and basic measurement errors.<\/li>\n<li>Use significant figures and rounding rules properly.<\/li>\n<\/ul>\n<p>These skills don\u2019t just help in a single topic\u2014they make nearly every physics problem easier. With consistent practice, unit logic becomes automatic, and your speed and accuracy improve across the entire NMAT Physics section.<\/p>\n<h1>Measurement and Units: Problem Sets with Answer Keys (NMAT Physics)<\/h1>\n<h2>How to Use These Problem Sets<\/h2>\n<p>These questions focus on the most tested skills in Measurement and Units for NMAT-level physics: SI base\/derived units,<br \/>\nmetric prefixes, unit conversion (including squared and cubed units), dimensional analysis, significant figures, and estimation.<br \/>\nTry solving first without looking at the answer keys. Then check your work and review the notes included in some solutions.<\/p>\n<h2>Problem Set 1: SI Units and Derived Units<\/h2>\n<ol>\n<li>Identify the SI base unit for each quantity:\n<ol type=\"a\">\n<li>Length<\/li>\n<li>Mass<\/li>\n<li>Time<\/li>\n<li>Temperature<\/li>\n<li>Electric current<\/li>\n<\/ol>\n<\/li>\n<li>Express the Newton (N) in SI base units.<\/li>\n<li>Express the Joule (J) in SI base units.<\/li>\n<li>Express the Pascal (Pa) in SI base units.<\/li>\n<li>A quantity has units kg\u00b7m<sup>2<\/sup>\/s<sup>3<\/sup>. What is its common SI unit name?<\/li>\n<li>Which of the following are dimensionless (no units)?\n<ol type=\"a\">\n<li>Strain<\/li>\n<li>Density<\/li>\n<li>Coefficient of friction<\/li>\n<li>Specific gravity<\/li>\n<li>Velocity<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h2>Answer Key: Problem Set 1<\/h2>\n<ol>\n<li>\n<ol type=\"a\">\n<li>meter (m)<\/li>\n<li>kilogram (kg)<\/li>\n<li>second (s)<\/li>\n<li>kelvin (K)<\/li>\n<li>ampere (A)<\/li>\n<\/ol>\n<\/li>\n<li>1 N = 1 kg\u00b7m\/s<sup>2<\/sup><\/li>\n<li>1 J = 1 N\u00b7m = (kg\u00b7m\/s<sup>2<\/sup>)\u00b7m = kg\u00b7m<sup>2<\/sup>\/s<sup>2<\/sup><\/li>\n<li>1 Pa = 1 N\/m<sup>2<\/sup> = (kg\u00b7m\/s<sup>2<\/sup>)\/m<sup>2<\/sup> = kg\/(m\u00b7s<sup>2<\/sup>)<\/li>\n<li>Watt (W), since 1 W = 1 J\/s = kg\u00b7m<sup>2<\/sup>\/s<sup>3<\/sup><\/li>\n<li>Dimensionless: (a) Strain, (c) Coefficient of friction, (d) Specific gravity<\/li>\n<\/ol>\n<h2>Problem Set 2: Metric Prefixes and Scientific Notation<\/h2>\n<ol>\n<li>Convert 7.2 km to meters.<\/li>\n<li>Convert 0.045 m to millimeters.<\/li>\n<li>Convert 3.6 \u00d7 10<sup>5<\/sup> \u03bcs to seconds.<\/li>\n<li>Write 0.00000082 in scientific notation.<\/li>\n<li>Write 5.07 \u00d7 10<sup>6<\/sup> in standard (decimal) form.<\/li>\n<li>Arrange from smallest to largest:\n<ol type=\"a\">\n<li>2.5 nm<\/li>\n<li>2.5 \u03bcm<\/li>\n<li>2.5 mm<\/li>\n<li>2.5 m<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h2>Answer Key: Problem Set 2<\/h2>\n<ol>\n<li>7.2 km = 7.2 \u00d7 10<sup>3<\/sup> m = 7200 m<\/li>\n<li>0.045 m = 0.045 \u00d7 1000 mm = 45 mm<\/li>\n<li>1 \u03bcs = 10<sup>-6<\/sup> s<br \/>\n3.6 \u00d7 10<sup>5<\/sup> \u03bcs = 3.6 \u00d7 10<sup>5<\/sup> \u00d7 10<sup>-6<\/sup> s = 3.6 \u00d7 10<sup>-1<\/sup> s = 0.36 s<\/li>\n<li>0.00000082 = 8.2 \u00d7 10<sup>-7<\/sup><\/li>\n<li>5.07 \u00d7 10<sup>6<\/sup> = 5,070,000<\/li>\n<li>Smallest \u2192 largest: 2.5 nm &lt; 2.5 \u03bcm &lt; 2.5 mm &lt; 2.5 m<\/li>\n<\/ol>\n<h2>Problem Set 3: Unit Conversions (Including Squared and Cubed)<\/h2>\n<ol>\n<li>Convert 90 km\/h to m\/s.<\/li>\n<li>Convert 15 m\/s to km\/h.<\/li>\n<li>Convert 250 cm to meters.<\/li>\n<li>Convert 2.5 m<sup>2<\/sup> to cm<sup>2<\/sup>.<\/li>\n<li>Convert 1.2 \u00d7 10<sup>6<\/sup> mm<sup>3<\/sup> to cm<sup>3<\/sup>.<\/li>\n<li>Convert 3.0 L to m<sup>3<\/sup>.<\/li>\n<li>Convert 4500 cm<sup>3<\/sup> to liters (L).<\/li>\n<li>Convert 1.8 g\/cm<sup>3<\/sup> to kg\/m<sup>3<\/sup>.<\/li>\n<\/ol>\n<h2>Answer Key: Problem Set 3<\/h2>\n<ol>\n<li>90 km\/h = 90 \u00d7 (1000\/3600) m\/s = 25 m\/s<\/li>\n<li>15 m\/s \u00d7 3.6 = 54 km\/h<\/li>\n<li>250 cm = 2.50 m<\/li>\n<li>1 m = 100 cm \u21d2 1 m<sup>2<\/sup> = (100)<sup>2<\/sup> cm<sup>2<\/sup> = 10,000 cm<sup>2<\/sup><br \/>\n2.5 m<sup>2<\/sup> = 2.5 \u00d7 10,000 = 25,000 cm<sup>2<\/sup><\/li>\n<li>1 cm = 10 mm \u21d2 1 cm<sup>3<\/sup> = (10 mm)<sup>3<\/sup> = 1000 mm<sup>3<\/sup><br \/>\n1.2 \u00d7 10<sup>6<\/sup> mm<sup>3<\/sup> \u00f7 1000 = 1.2 \u00d7 10<sup>3<\/sup> cm<sup>3<\/sup> = 1200 cm<sup>3<\/sup><\/li>\n<li>1 L = 10<sup>-3<\/sup> m<sup>3<\/sup> \u21d2 3.0 L = 3.0 \u00d7 10<sup>-3<\/sup> m<sup>3<\/sup><\/li>\n<li>1000 cm<sup>3<\/sup> = 1 L \u21d2 4500 cm<sup>3<\/sup> = 4.5 L<\/li>\n<li>1 g\/cm<sup>3<\/sup> = 1000 kg\/m<sup>3<\/sup> \u21d2 1.8 g\/cm<sup>3<\/sup> = 1800 kg\/m<sup>3<\/sup><\/li>\n<\/ol>\n<h2>Problem Set 4: Dimensional Analysis and Formula Checking<\/h2>\n<ol>\n<li>Show that the unit of acceleration is m\/s<sup>2<\/sup> using the definition of acceleration.<\/li>\n<li>A student proposes the formula for distance: d = vt<sup>2<\/sup>. Is it dimensionally correct? Explain briefly.<\/li>\n<li>Using dimensional analysis, determine the dimensions of pressure in terms of M, L, and T.<\/li>\n<li>The period T of a simple pendulum depends on length L and gravitational acceleration g.<br \/>\nUse dimensional analysis to find how T depends on L and g (ignore constants).<\/li>\n<li>If energy E has dimensions ML<sup>2<\/sup>T<sup>-2<\/sup>, what are the dimensions of power P = E\/t?<\/li>\n<\/ol>\n<h2>Answer Key: Problem Set 4<\/h2>\n<ol>\n<li>Acceleration a = \u0394v\/\u0394t. Velocity has units m\/s. Dividing by s gives (m\/s)\/s = m\/s<sup>2<\/sup>.<\/li>\n<li>Check dimensions: left side d is [L]. Right side v t<sup>2<\/sup> is [L\/T]\u00b7[T<sup>2<\/sup>] = [L\u00b7T]. Not equal to [L]. So it is NOT dimensionally correct.<\/li>\n<li>Pressure = Force\/Area. Force is [M L T<sup>-2<\/sup>]. Area is [L<sup>2<\/sup>].<br \/>\nPressure dimensions = [M L T<sup>-2<\/sup>]\/[L<sup>2<\/sup>] = [M L<sup>-1<\/sup> T<sup>-2<\/sup>].<\/li>\n<li>Assume T \u221d L<sup>a<\/sup> g<sup>b<\/sup>. Dimensions: [T] = [L]<sup>a<\/sup> ([L T<sup>-2<\/sup>])<sup>b<\/sup> = [L]<sup>a+b<\/sup>[T]<sup>-2b<\/sup>.<br \/>\nMatch exponents: -2b = 1 \u21d2 b = -1\/2. Then a + b = 0 \u21d2 a = 1\/2.<br \/>\nTherefore T \u221d \u221a(L\/g).<\/li>\n<li>Power P = E\/t \u21d2 [P] = [M L<sup>2<\/sup> T<sup>-2<\/sup>]\/[T] = [M L<sup>2<\/sup> T<sup>-3<\/sup>].<\/li>\n<\/ol>\n<h2>Problem Set 5: Significant Figures, Rounding, and Measurement Concepts<\/h2>\n<ol>\n<li>How many significant figures are in 0.00450?<\/li>\n<li>How many significant figures are in 2050 (no decimal shown)?<\/li>\n<li>Round 12.349 to 3 significant figures.<\/li>\n<li>Multiply and report with correct significant figures: (2.4)(3.56)<\/li>\n<li>Add and report with correct decimal places: 18.2 + 0.045 + 1.1<\/li>\n<li>Explain briefly: what is the difference between accuracy and precision?<\/li>\n<li>A miscalibrated balance always reads 2 g heavier than the true mass. Is this systematic or random error?<\/li>\n<\/ol>\n<h2>Answer Key: Problem Set 5<\/h2>\n<ol>\n<li>0.00450 has 3 significant figures (4, 5, and the trailing 0 after the decimal).<\/li>\n<li>2050 (no decimal shown) is ambiguous, but typically counted as 3 significant figures (2, 0, 5). The last 0 may or may not be significant without a decimal point.<\/li>\n<li>12.349 \u2192 3 significant figures = 12.3 (since the next digit is 4).<\/li>\n<li>(2.4)(3.56) = 8.544. Fewest s.f. is 2 (from 2.4). Final = 8.5<\/li>\n<li>18.2 + 0.045 + 1.1 = 19.345. Least decimal places is 1 (from 18.2 and 1.1). Final = 19.3<\/li>\n<li>Accuracy is closeness to the true value; precision is closeness of repeated measurements to each other.<\/li>\n<li>Systematic error (consistent bias of +2 g).<\/li>\n<\/ol>\n<h2>Problem Set 6: Mixed NMAT-Style Questions (Speed + Unit Sense)<\/h2>\n<ol>\n<li>A runner covers 400 m in 50 s. What is the average speed in m\/s?<\/li>\n<li>The density of a material is 2.7 g\/cm<sup>3<\/sup>. What is it in kg\/m<sup>3<\/sup>?<\/li>\n<li>Convert 5.0 \u00d7 10<sup>-2<\/sup> m to micrometers (\u03bcm).<\/li>\n<li>A force of 12 N acts over a distance of 0.50 m. How much work is done?<\/li>\n<li>A pressure of 2.0 \u00d7 10<sup>5<\/sup> Pa is applied over an area of 0.10 m<sup>2<\/sup>. What is the force?<\/li>\n<li>Which has the larger magnitude: 3.6 \u00d7 10<sup>4<\/sup> mm or 3.6 \u00d7 10<sup>1<\/sup> m?<\/li>\n<li>A cube has side length 5.0 cm. Find its volume in m<sup>3<\/sup>.<\/li>\n<li>If v has units m\/s and p has units kg\u00b7m\/s, what quantity could p represent?<\/li>\n<\/ol>\n<h2>Answer Key: Problem Set 6<\/h2>\n<ol>\n<li>v = d\/t = 400\/50 = 8 m\/s<\/li>\n<li>2.7 g\/cm<sup>3<\/sup> = 2700 kg\/m<sup>3<\/sup><\/li>\n<li>5.0 \u00d7 10<sup>-2<\/sup> m = 0.05 m. Since 1 m = 10<sup>6<\/sup> \u03bcm, 0.05 m = 0.05 \u00d7 10<sup>6<\/sup> \u03bcm = 5.0 \u00d7 10<sup>4<\/sup> \u03bcm<\/li>\n<li>W = Fd = 12 \u00d7 0.50 = 6.0 J<\/li>\n<li>F = PA = (2.0 \u00d7 10<sup>5<\/sup>)(0.10) = 2.0 \u00d7 10<sup>4<\/sup> N<\/li>\n<li>3.6 \u00d7 10<sup>4<\/sup> mm = 3.6 \u00d7 10<sup>4<\/sup> \u00d7 10<sup>-3<\/sup> m = 3.6 \u00d7 10<sup>1<\/sup> m = 36 m.<br \/>\nThey are equal.<\/li>\n<li>Side = 5.0 cm = 5.0 \u00d7 10<sup>-2<\/sup> m. Volume = s<sup>3<\/sup> = (5.0 \u00d7 10<sup>-2<\/sup>)<sup>3<\/sup> m<sup>3<\/sup> = 125 \u00d7 10<sup>-6<\/sup> = 1.25 \u00d7 10<sup>-4<\/sup> m<sup>3<\/sup><\/li>\n<li>p = kg\u00b7m\/s is momentum (p = mv).<\/li>\n<\/ol>\n<h2>Bonus: Quick Conversion &amp; Unit Facts (Must-Memorize)<\/h2>\n<ul>\n<li>1 hour = 3600 s<\/li>\n<li>1 km = 1000 m<\/li>\n<li>1 m\/s = 3.6 km\/h<\/li>\n<li>1 L = 1000 cm<sup>3<\/sup> = 10<sup>-3<\/sup> m<sup>3<\/sup><\/li>\n<li>1 g\/cm<sup>3<\/sup> = 1000 kg\/m<sup>3<\/sup><\/li>\n<li>1 N = kg\u00b7m\/s<sup>2<\/sup><\/li>\n<li>1 J = N\u00b7m = kg\u00b7m<sup>2<\/sup>\/s<sup>2<\/sup><\/li>\n<li>1 Pa = N\/m<sup>2<\/sup> = kg\/(m\u00b7s<sup>2<\/sup>)<\/li>\n<\/ul>\n<blockquote class=\"wp-embedded-content\" data-secret=\"oNCdUZXBZp\"><p><a href=\"https:\/\/3d-universal.com\/en\/blogs\/nmat-physics-review.html\">NMAT Physics Review: NMAT Study Guide<\/a><\/p><\/blockquote>\n<p><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"&#8220;NMAT Physics Review: NMAT Study Guide&#8221; &#8212; Study English at 3D ACADEMY, a Language School in Cebu, Philippines\" src=\"https:\/\/3d-universal.com\/en\/blogs\/nmat-physics-review.html\/embed#?secret=82HbhbImD7#?secret=oNCdUZXBZp\" data-secret=\"oNCdUZXBZp\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<blockquote class=\"wp-embedded-content\" data-secret=\"rLO1j3DMd8\"><p><a href=\"https:\/\/3d-universal.com\/en\/philippines-university-guide\/nmat-study-guide\">NMAT Study Guide: Complete Preparation Guide for Medical School in the Philippines<\/a><\/p><\/blockquote>\n<p><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"&#8220;NMAT Study Guide: Complete Preparation Guide for Medical School in the Philippines&#8221; &#8212; Study English at 3D ACADEMY, a Language School in Cebu, Philippines\" src=\"https:\/\/3d-universal.com\/en\/philippines-university-guide\/nmat-study-guide\/embed#?secret=6j3V8cbeiZ#?secret=rLO1j3DMd8\" data-secret=\"rLO1j3DMd8\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe><\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":21091,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_kad_blocks_custom_css":"","_kad_blocks_head_custom_js":"","_kad_blocks_body_custom_js":"","_kad_blocks_footer_custom_js":"","footnotes":""},"categories":[117],"tags":[],"class_list":["post-21088","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-nmat-physics-review"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v25.6 (Yoast SEO v25.6) - 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