Chapter 1 - Physical Quantities and Measurements (Flashcards)

A set of practice flashcards covering physical quantities, measurements, units, dimensional analysis, vectors, and errors/significant figures based on the provided lecture notes.

What are base quantities?

Quantities that cannot be expressed as other quantities.

What are derived quantities?

Quantities that can be expressed in terms of base quantities.

List the SI base quantities and their SI units.

Length (distance) – metre (m); Time – second (s); Mass – kilogram (kg); Temperature – kelvin (K); Electrical current – ampere (A).

What is the SI unit of area?

Square metre (m^2).

What is the SI unit of volume?

Cubic metre (m^3).

What is the SI unit of density?

Kilogram per cubic metre (kg/m^3).

What is the SI unit of speed?

Metre per second (m/s).

What is the SI unit of acceleration?

Metre per second squared (m/s^2).

What is the SI unit of velocity?

Metre per second (m/s).

What is the SI unit of force?

Newton (N) = kg·m/s^2.

What is the SI unit of work?

Joule (J) = kg·m^2/s^2.

What is the SI unit of angle?

Radian (rad) — dimensionless unit.

Is the index of refraction a quantity with a unit?

No; it has no unit (dimensionless).

Is multiplying 2 cm by 2 cm a valid unit operation, and what is the result?

Yes; 2 cm × 2 cm = 4 cm^2.

When adding measurements, what must be true about the units?

The units must be the same; convert if necessary (e.g., 50 cm + 1 m = 150 cm).

What is standard form in quantities, and what are the constraints?

A × 10^n with 1 ≤ A < 10 and n an integer.

What is 1 km in metres?

1 km = 10^3 m.

What is 1 μg in grams?

1 μg = 10^-6 g.

What is 1 ns in seconds?

1 ns = 10^-9 s.

What is 1 km^2 in m^2?

1 km^2 = 10^6 m^2 (area prefixes square).

What is the recommended method to convert complex units?

Multiply by unity fractions, cancel original units, apply desired units, apply correct conversion values, raise powers if necessary, and repeat for other units.

Give an example of a direct SI prefix conversion (simple unit).

1 nm = 1 × 10^-9 m; 1 cm^2 × 1 m/100 cm^2 = 1 × 10^-4 m^2.

What is the formula for average speed and which base quantities does it involve?

v_avg = d/t; involves distance (length) and time.

What is the unit for distance/length and time that make up average speed?

Distance (length) and Time.

What is the dimension of velocity?

Dimension: [L][T]^-1; SI unit: m/s.

What does it mean for a quantity to be dimensionless?

It has no physical dimension or unit.

In dimensional analysis, if a = b v, what is the dimension of b?

b has dimension T^-1 (inverse time).

In the equation a = k m v^2, what is the SI unit (or dimension) of k?

k has dimension M^-1 L^-1 (SI unit: kg^-1 m^-1).

In the velocity equation v = m x^2 + n x, what are the dimensions of m and n?

m: L^-1 T^-1 (unit: m^-1 s^-1); n: T^-1 (unit: s^-1).

What is the difference between scalar and vector quantities?

Scalar quantities have magnitude only; vector quantities have magnitude and direction.

What is a resultant vector?

The vector from the tail of the first vector to the head of the final vector; found via graphical or algebraic methods.

Are vector addition and subtraction commutative?

Vector addition is commutative (A + B = B + A); vector subtraction is not generally commutative.

What are the outcomes of dot and cross products?

Dot product yields a scalar; cross product yields a vector.

What is the Pythagorean theorem for vector components?

For components: F^2 = Fx^2 + Fy^2 (or r^2 = x^2 + y^2 in 2D).

What is the volume of a rectangular block with dimensions 0.40 m × 0.30 m × 0.50 m?

Volume = 0.060 m^3.

How do you compute density given mass m and volume V?

Density = m / V; e.g., 162 kg / 0.060 m^3 ≈ 2.7 × 10^3 kg/m^3.

What are the basic rules for significant figures with exact numbers?

Exact numbers have unlimited significant figures.

What are the significant figure rules for zeros?

Leading zeros are not significant; captive zeros are significant; trailing zeros are significant only with a decimal point.

How many significant figures does multiplication/division preserve?

The result has as many significant figures as the factor with the fewest significant figures.

How many decimal places does addition/subtraction preserve?

The result has the same number of decimal places as the quantity with the fewest decimal places.

What is the volume and density of the example block given in the notes?

Volume: 0.060 m^3; Density: approximately 2.7 × 10^3 kg/m^3.