Scalar or vector? Read every quantity carefully
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Video lessonScalars vs vectors · SI base units · significant figures
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Scalars vs vectors
A scalar has magnitude only (mass, time, speed). A vector has magnitude and direction (displacement, velocity, force).
A scalar has magnitude only (mass, time, speed). A vector has magnitude and direction (displacement, velocity, force).
SI base quantities
Seven base units: m (length), kg (mass), s (time), A (current), K (temperature), mol (amount), cd (luminous intensity). All other units are derived.
Seven base units: m (length), kg (mass), s (time), A (current), K (temperature), mol (amount), cd (luminous intensity). All other units are derived.
Significant figures
Keep the least precise count when multiplying or dividing; keep the least decimal places when adding or subtracting.
Keep the least precise count when multiplying or dividing; keep the least decimal places when adding or subtracting.
Vector addition
Triangle rule (head-to-tail) or parallelogram rule. The order does not change magnitude, but direction is set relative to a chosen frame.
Triangle rule (head-to-tail) or parallelogram rule. The order does not change magnitude, but direction is set relative to a chosen frame.
Worked example
A car travels 30 km due east, then 40 km due north. The trip takes 2.0 h. Find the magnitude and direction of the car's average velocity.
Resolve the motion into east and north components first, then combine them with the Pythagorean theorem.
Show solution
Use the components $v_x = 30/2.0 = 15$ km/h and $v_y = 40/2.0 = 20$ km/h. The magnitude is $|\vec{\bar{v}}| = \sqrt{15^2 + 20^2} = 25$ km/h. The direction is $\theta = \arctan(20/15) \approx 53°$ north of east.