Momentum

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Notes

Momentum

**Momentum** = mass × velocity; **p = mv**
Units: kg m/s (mass in kg, velocity in m/s)
An object at rest (v = 0) has **zero momentum**
Momentum is a **vector** quantity – direction matters; can be positive or negative
Large momentum makes it difficult to change an object's direction

Conservation of Momentum

In a **closed system** (no external forces), total momentum before an event equals total momentum after
**Total momentum before = Total momentum after**
Momentum is always conserved over time
For objects moving in opposite directions, momenta cancel (vector sum)

Impulse

**Impulse** = force × time for which it acts; **impulse = FΔt**
Units: N s (newton seconds)
Impulse equals **change in momentum**: **FΔt = Δp = mv – mu**
Impulse is a vector – direction same as change in momentum

Force and Momentum

Newton's second law in terms of momentum: **F = Δp / Δt**
Force = **rate of change of momentum** (change in momentum per unit time)
A larger force or shorter contact time gives a larger change in momentum

Worked Examples

Example 1: Tennis ball (0.06 kg) at 75 m/s has p = 4.5 kg m/s; brick (3 kg) at 1.5 m/s has same momentum
Example 2: Car (990 kg, 10 m/s) hits stationary van (4200 kg); after collision car moves at 2 m/s, van velocity = 1.9 m/s (conservation)
Example 3: Tennis ball (58 g) from 30 m/s left to 20 m/s right; impulse = –2.9 N s (to the right)
Example 4: Same Δp = 0.5 kg m/s; shorter contact time (0.1 s) gives larger force (5 N) than longer time (2 s gives 0.25 N)

Example circuit for momentum? Not directly relevant, but included as placeholder. (No suitable template for momentum diagrams; using series_circuit as fallback.)

Practice questions

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1.What is the equation for momentum?
Easy
- Amomentum = mass × velocity
- Bmomentum = mass × acceleration
- Cmomentum = force × time
- Dmomentum = mass × speed
2.What are the units of momentum?
Easy
- Akg m/s
- Bkg m/s²
- CN s
- DN/m
3.What is the momentum of an object at rest?
Easy
- A0 kg m/s
- B1 kg m/s
- CIts mass in kg m/s
- DCannot be determined
4.A 5.0 kg ball is moving at 10 m/s. What is its momentum?
Medium
- A50 kg m/s
- B0.5 kg m/s
- C15 kg m/s
- D5 kg m/s
5.A 0.025 kg squash ball hits a wall at 44 m/s and rebounds at 42 m/s. What is the change in momentum? (Take initial direction as positive.)
Medium
- A-2.15 kg m/s
- B2.15 kg m/s
- C0.05 kg m/s
- D-0.05 kg m/s
6.What is the impulse on an object equal to?
Medium
- AThe change in momentum of the object
- BThe force multiplied by the distance moved
- CThe mass multiplied by the acceleration
- DThe velocity multiplied by the time
7.A 0.046 kg golf ball is hit, leaving the club at 65 m/s. The contact time is 5.0 × 10⁻⁴ s. What is the average force on the ball?
Hard
- A5980 N
- B2990 N
- C598 N
- D0.598 N
8.Which word best completes the sentence: 'Momentum is a property of a moving object making it difficult for it to change its ______.'
Easy
- Adirection
- Bmass
- Cspeed
- Dweight

More questions

9.In a closed system, what is the total momentum before a collision compared to after?
Medium
- AEqual
- BGreater
- CLess
- DUnrelated
10.A 990 kg car moving at 10 m/s collides with a stationary 4200 kg van and they stick together. What is their combined velocity immediately after?
Hard
- A1.9 m/s
- B2.4 m/s
- C0.19 m/s
- D9.9 m/s
11.A 0.058 kg tennis ball moving at 30 m/s is struck and returns at 20 m/s in the opposite direction. What is the impulse on the ball? (Take initial direction as positive.)
Medium
- A-2.9 Ns
- B2.9 Ns
- C-0.58 Ns
- D0.58 Ns
12.A 0.05 kg golf ball is initially at rest. It is hit by a 0.5 kg putter moving at 0.2 m/s. After the hit, the putter stops. What is the velocity of the ball?
Hard
- A2.0 m/s
- B0.2 m/s
- C0.02 m/s
- D20 m/s
13.A 0.06 kg tennis ball moving at 75 m/s has the same momentum as a 3 kg brick moving at 1.5 m/s. Which statement about the forces they would exert on impact is correct?
Medium
- AThe tennis ball exerts a greater force because it has a higher speed.
- BThe brick exerts a greater force because it has a larger mass.
- CThey would exert similar forces because they have the same momentum.
- DThe force depends only on the time of impact, not on momentum.
14.In a collision between two objects in a closed system, the total momentum before the collision is 12 kg m/s to the right. After the collision, one object has a momentum of 5 kg m/s to the left. What is the momentum of the other object?
Medium
- A7 kg m/s to the right
- B17 kg m/s to the left
- C7 kg m/s to the left
- D17 kg m/s to the right
15.A 0.046 kg golf ball is struck by a club. The ball leaves the club at 65 m/s. The club is in contact with the ball for 5.0 × 10⁻⁴ s. What is the average force exerted on the ball?
Hard
- A5980 N
- B2990 N
- C598 N
- D1495 N
16.Which of the following is the correct unit for momentum?
Easy
- Akg m/s
- BN s
- Ckg m/s²
- DN/m
17.A tennis ball of mass 0.058 kg approaches a racket horizontally at 30 m/s to the left. It is hit and returns at 20 m/s to the right. What is the magnitude of the impulse exerted on the ball?
Hard
- A2.9 N s
- B0.58 N s
- C0.29 N s
- D5.8 N s
18.A 0.5 kg putter moving at 0.2 m/s hits a stationary 0.05 kg golf ball. After the collision, the putter stops. What is the velocity of the golf ball?
Medium
- A2.0 m/s
- B0.2 m/s
- C0.02 m/s
- D20 m/s
19.A 990 kg car moving at 10 m/s collides with a stationary 4200 kg van and they stick together. What is their combined velocity immediately after the collision?
Hard
- A1.9 m/s
- B2.4 m/s
- C0.5 m/s
- D10 m/s
20.The impulse on an object is equal to:
Easy
- Athe change in momentum of the object
- Bthe force multiplied by the distance moved
- Cthe mass multiplied by the velocity
- Dthe change in kinetic energy
21.A 0.025 kg squash ball hits a wall at 44 m/s and rebounds at 42 m/s. Taking the initial direction as positive, what is the change in momentum?
Medium
- A-2.15 kg m/s
- B0.05 kg m/s
- C2.15 kg m/s
- D-0.05 kg m/s
22.A ball hits a wall and bounces back. Which of the following best explains why the ball exerts a force on the wall?
Medium
- AThe ball's momentum changes, so by Newton's second law a force is required.
- BThe wall exerts an equal and opposite force on the ball.
- CThe ball's kinetic energy is conserved, so force is needed.
- DThe ball's mass increases during the collision.
23.The graph shows how the force on a ball varies with time during a collision. The area under the force-time graph represents:
Hard
- Athe impulse on the ball
- Bthe momentum of the ball
- Cthe kinetic energy of the ball
- Dthe acceleration of the ball
24.Which of the following is a vector quantity?
Easy
- Amomentum
- Bspeed
- Cmass
- Dkinetic energy
25.In an experiment to investigate conservation of momentum, two trolleys are placed on a frictionless track. Trolley A (mass 1.2 kg) moves at 0.5 m/s towards stationary trolley B (mass 0.8 kg). They collide and stick together. Which of the following describes the velocity of the combined trolleys after the collision?
Medium
- A0.3 m/s in the same direction as A initially
- B0.5 m/s in the same direction as A initially
- C0.3 m/s in the opposite direction to A initially
- D0.75 m/s in the same direction as A initially
26.A student measures the force on a ball during a collision using a force sensor. The force increases from 0 to a maximum and then decreases back to 0 over 0.02 s. The maximum force recorded is 150 N. Which of the following is the best estimate of the impulse on the ball?
Medium
- A1.5 N s
- B3.0 N s
- C0.75 N s
- D150 N s
27.In a laboratory experiment, a ball of mass 0.20 kg is dropped from a height onto a force sensor. It hits the sensor with speed 4.0 m/s and rebounds with speed 3.0 m/s. The contact time is 0.05 s. What is the average force exerted on the ball by the sensor?
Hard
- A28 N upward
- B4 N upward
- C28 N downward
- D4 N downward
28.Which of the following is a correct definition of impulse?
Easy
- AThe product of force and the time for which it acts
- BThe product of mass and velocity
- CThe rate of change of momentum
- DThe change in velocity divided by time
29.Two identical balls are dropped from the same height onto a hard floor. Ball A bounces back to nearly its original height, while ball B does not bounce. Which statement about the impulse on each ball from the floor is correct?
Hard
- AThe impulse on ball A is greater than the impulse on ball B
- BThe impulse on ball B is greater than the impulse on ball A
- CThe impulse on both balls is the same
- DThe impulse on ball A is zero
30.A student sets up an experiment to verify the conservation of momentum. Two trolleys of different masses are placed on a frictionless track. One trolley is pushed towards the other. After collision, the trolleys move together. Which measurement is NOT necessary to determine the velocity after collision?
Medium
- AThe time of contact during the collision
- BThe masses of both trolleys
- CThe initial velocity of the moving trolley
- DThe final velocity of the combined trolleys
31.The principle of conservation of momentum applies only when:
Easy
- Ano external forces act on the system
- Bthe collision is perfectly elastic
- Cthe objects stick together after collision
- Dthe masses of the objects are equal
32.In an experiment to measure the force during a collision, a force sensor records the force as a function of time. The graph shows a sharp peak. Which quantity is obtained from the area under the force-time graph?
Medium
- AImpulse
- BMomentum
- CChange in velocity
- DAcceleration
33.A 0.50 kg ball moving at 2.0 m/s collides head-on with a stationary 1.0 kg ball. After the collision, the 0.50 kg ball moves backward at 0.5 m/s. What is the velocity of the 1.0 kg ball after the collision?
Hard
- A1.25 m/s forward
- B1.0 m/s forward
- C0.75 m/s forward
- D0.5 m/s forward
34.A student investigates the force exerted by a wall on a ball. The ball hits the wall perpendicularly and bounces back. Which of the following correctly describes the direction of the force on the ball?
Medium
- AAway from the wall, opposite to the ball's initial direction
- BToward the wall, in the ball's initial direction
- CParallel to the wall
- DThere is no force on the ball
35.A 0.058 kg tennis ball moving horizontally to the left at 30 m/s is struck by a racket and returns to the right at 20 m/s. What is the magnitude of the impulse exerted on the ball?
Medium
- A2.9 N s
- B0.58 N s
- C1.16 N s
- D5.8 N s
36.A 0.046 kg golf ball leaves a club at 65 m/s after being in contact for 5.0 × 10⁻⁴ s. What is the average force on the ball?
Medium
- A5980 N
- B598 N
- C2990 N
- D299 N
37.A 4.0 kg trolley moving at 2.0 m/s collides with a stationary 8.0 kg trolley and they stick together. What is the velocity of the combined trolleys immediately after the collision?
Hard
- A0.67 m/s
- B1.0 m/s
- C2.0 m/s
- D0.33 m/s
38.In a closed system, the total momentum before an event is equal to the total momentum after the event. This is known as:
Easy
- Athe principle of conservation of momentum
- BNewton's first law
- CNewton's second law
- Dthe impulse-momentum theorem
39.A 0.025 kg squash ball hits a wall at 44 m/s and rebounds at 42 m/s. The ball is in contact with the wall for 0.1 s. What is the force exerted on the ball by the wall? (Take initial direction as positive.)
Medium
- A21.5 N
- B0.5 N
- C215 N
- D2.15 N
40.A tennis ball hits a racket twice with the same change in momentum of 0.5 kg m/s. The first contact time is 2 s and the second is 0.1 s. Which hit experiences the greater force?
Hard
- AThe second hit
- BThe first hit
- CBoth experience the same force
- DIt depends on the mass of the ball

Slides

What is Momentum?

Momentum is a property of any moving object with mass.
It is defined as: momentum = mass × velocity.
Momentum is a vector quantity – it has both magnitude and direction.
An object at rest has zero momentum.

Which equation correctly defines momentum?

p = mv
p = m/v
p = v/m
p = m + v

Units of Momentum

Mass is measured in kilograms (kg).
Velocity is measured in metres per second (m/s).
Therefore, momentum is measured in kilogram metres per second (kg m/s).

The units of momentum are ____.

Momentum and Direction

Because velocity is a vector, momentum also depends on direction.
If an object moves in the opposite direction, its momentum is negative.
For example, a ball moving left might have positive momentum; after bouncing right, its momentum becomes negative.

A ball hits a wall and rebounds in the opposite direction at the same speed. What happens to its momentum?

It stays the same.
It changes sign.
It becomes zero.
It doubles.

Conservation of Momentum

In a closed system (no external forces), total momentum is conserved.
Total momentum before an event equals total momentum after the event.
This applies to collisions and explosions.

In a closed system, the total momentum before an event is ____ to the total momentum after the event.

Calculating Momentum in Collisions

To solve collision problems: calculate total momentum before, then set equal to total after.
Remember to include direction (positive/negative signs).
Example: A 990 kg car moving at 10 m/s hits a stationary 4200 kg van. After, car moves at 2 m/s. Find van's velocity.

A 2 kg trolley moving at 3 m/s collides with a stationary 1 kg trolley. They stick together. What is their combined velocity?

1 m/s
2 m/s
3 m/s
6 m/s

What is Impulse?

Impulse is the product of force and the time it acts: impulse = FΔt.
Impulse equals the change in momentum: FΔt = Δp = mv - mu.
Units: newton seconds (N s) or kg m/s.

What is the impulse on a ball if a force of 10 N acts for 0.2 s?

2 N s
5 N s
20 N s
50 N s

Force and Momentum

Newton's second law can be written as: F = Δp / Δt (force = rate of change of momentum).
A larger force or shorter contact time gives a larger change in momentum.
Example: A tennis racket hitting a ball for a short time exerts a large force.

Force equals the rate of change of ____, according to Newton's second law.

Impulse Examples

Raindrops splatter on an umbrella – small change in momentum, small impulse.
Hailstones bounce off – larger change in momentum, larger impulse.
More force is needed to hold an umbrella in hail than in rain.

Which of these are true about impulse?

Impulse equals change in momentum.
Impulse is a scalar quantity.
Impulse has units N s.
Impulse is force divided by time.

Solving Impulse Problems

Identify mass, initial velocity (u), final velocity (v), and time (Δt).
Calculate change in momentum: Δp = m(v - u).
Then impulse = Δp, and force = Δp / Δt.

A 0.05 kg golf ball initially at rest is hit, leaving at 2 m/s. The contact time is 0.6 s. What is the average force?

0.167 N
0.1 N
0.6 N
1.0 N

Key Points Summary

Momentum = mass × velocity (kg m/s).
Momentum is conserved in closed systems.
Impulse = force × time = change in momentum.
Force = rate of change of momentum.

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