8867 / 2027
Motion and Forces overview

Lesson 4 of 6

Inertia and linear momentum

  • I can explain mass as the property that resists a change in motion: inertia.Syllabus

    Syllabus 8867, 3(f). Explain mass as the property that resists a change in motion: inertia.

  • I can define and use linear momentum as mass multiplied by velocity.Syllabus

    Syllabus 8867, 3(g). Define and use linear momentum as mass multiplied by velocity.

Make a guess. You are not marked.

A 1000 kg car and a 60 kg cyclist both move at 10 m/s. Which needs the larger force to stop in the same time, and why?

  1. The cyclist, because a smaller body has less grip on the road.
  2. The car, because its momentum, 10000 kg m/s, is far larger.
  3. Neither, because they have the same velocity.
Show the answer

The car, because its momentum, 10000 kg m/s, is far larger.

Force = change in momentum / time. The car has 1000 x 10 = 10000 kg m/s against the cyclist's 600 kg m/s, so stopping it in the same time needs a much larger force.

Mass describes a body's resistance to a change in motion. Momentum combines that mass with its velocity, including direction.

Inertia concerns a change in motion

Mass measures inertia. Under the same resultant force, a body of greater constant mass has a smaller acceleration. Inertia is not a resistance to motion itself: a moving body does not need a forward resultant force merely to keep a constant velocity.

Mass is a scalar measured in kg. Weight is a gravitational force measured in N. We treat the laboratory frame as approximately inertial, so the ordinary force laws apply without adding a separate backward "inertia force" to a body's diagram.

Linear momentum is mass times velocity

p = mv

Momentum is a vector in the direction of velocity. In one dimension, retain the velocity's sign. If velocity is given by several components, multiply every component by the scalar mass.

Its unit is kg m/s, also written N s: since N = kg m s-2, multiplying by s gives kg m s-1. Momentum is not a force; N s and N describe different quantities.

Momentum through a reversal

Subtract final and initial vectors in order

A 1.20 kg body changes velocity from +3.0 m/s to -2.0 m/s along the same axis.

Initial momentum = 1.20(+3.0) = +3.6 kg m/s.
Final momentum = 1.20(-2.0) = -2.4 kg m/s.

Change = final - initial:
Δp = -2.4 - (+3.6) = -6.0 kg m/s.

Subtract signed momentum, including the reversal

Positive 3.6 changes to negative 2.4 kilogram metres per secondThree separate arrow rows use forty-five drawing units per kilogram metre per second, with right positive. In the first row initial momentum points right with magnitude 3.6. In the second final momentum points left with magnitude 2.4. The two share a marked zero coordinate. In the third, the change arrow starts at the initial momentum tip coordinate and ends at the final momentum tip coordinate, so it points left with magnitude six. This is final minus initial, not a subtraction of the two magnitudes.Zero coordinateInitial p = +3.6 kg m/sFinal p = -2.4 kg m/sChange = -6.0 kg m/sInitial tipFinal tip

For the 1.20 kg body, Δp = -2.4 - (+3.6) = -6.0 kg m/s. The change is leftwards. If this occurs over 0.50 s, the average resultant force is -12 N; that alone does not establish a constant instantaneous force.

Initial and final momentum arrows refer to different times. Their vector difference points in the negative direction and has magnitude 6.0 kg m/s. It is not the difference of the speed magnitudes.

Momentum can be zero at an instant while changing at that instant. At the top of a vertical flight, velocity and momentum are zero, but gravity still produces downward acceleration and a changing momentum.

Check your understanding

A 1.20 kg body changes velocity from +3.0 m/s to -2.0 m/s. What is its change in momentum?

  1. -6.0 kg m/s
  2. +6.0 kg m/s
  3. -1.2 kg m/s
Show the answer

-6.0 kg m/s

Final minus initial gives 1.20(-2.0) - 1.20(+3.0) = -2.4 - 3.6 = -6.0 kg m/s. The sign includes the reversal.