Practise Momentum is a property of moving objects. 11 exam-style questions on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Momentum is a property of every moving object: momentum = mass × velocity. It is a vector, so direction matters. This is Higher tier content. Expect calculations with p = m v, often as the first part of a collision question.
Grade by grade
What you need to be able to do, from the first marks up to the top grade.
5
Recall the momentum equation p = m vMomentum (kg m/s) = mass (kg) × velocity (m/s).
6
Calculate momentumFor example, 0.16 kg × 25 m/s = 4.0 kg m/s.
6
Rearrange p = m v for mass or velocitym = p ÷ v and v = p ÷ m.
7
Explain that momentum is a vectorMomentum has the same direction as the velocity; opposite directions have opposite signs.
7
Compare the momentum of different objectsA slow, heavy object can have more momentum than a fast, light one.
8
Calculate a change in momentum, including directionFor a rebound, change in momentum = m v − m u with the correct signs.
Notes
What momentum is
Momentum is a property of moving objects.
momentum = mass × velocity: p = m v
p in kilogram metres per second (kg m/s), m in kilograms (kg), v in metres per second (m/s).
A stationary object has zero momentum.
Momentum is a vector
Momentum has the same direction as the velocity.
Choose one direction as positive. An object moving the opposite way has negative momentum: a 2.0 kg ball moving at 3.0 m/s to the left has p = −6.0 kg m/s if right is positive.
Two identical objects moving towards each other at the same speed have a total momentum of zero.
Comparing momentum
Momentum depends on both mass and velocity. A 1500 kg car moving at 2.0 m/s (3000 kg m/s) has more momentum than a 70 kg sprinter at 10 m/s (700 kg m/s).
Doubling the mass, or doubling the velocity, doubles the momentum.
Changes in momentum grade 8+
Change in momentum = final momentum − initial momentum = m v − m u.
Example: a 0.50 kg ball hits a wall at 6.0 m/s and rebounds at 4.0 m/s. Taking 'towards the wall' as positive: change = 0.50 × (−4.0) − 0.50 × 6.0 = −5.0 kg m/s, so 5.0 kg m/s away from the wall.
Because the direction reverses, the size of the change (5.0) is bigger than either the initial (3.0) or the final (2.0) momentum.
Cheatsheet
p = m v (momentum = mass × velocity)
Units: p in kg m/s, m in kg, v in m/s
Momentum is a vector, in the same direction as the velocity
Opposite directions: opposite signs
Stationary object: p = 0
Change in momentum = m v − m u (use signs for direction) grade 8+
How to answer each type of question
Calculate momentum
2 marks6
Check the mass is in kg and the velocity in m/s.
Write p = m v and substitute.
Give the unit kg m/s.
Example. A lorry of mass 12 000 kg travels at 15 m/s. Calculate the momentum of the lorry.
Show the model answer
p = 12 000 × 15 (1) p = 180 000 kg m/s (1)
Rearrange p = m v
3 marks6
Convert grams to kilograms.
Rearrange: v = p ÷ m or m = p ÷ v.
Give the unit.
Example. A cricket ball has a mass of 160 g and a momentum of 5.6 kg m/s. Calculate the velocity of the ball.
Show the model answer
m = 160 g = 0.160 kg (1) v = 5.6 ÷ 0.160 (1) v = 35 m/s (1)
Compare the momentum of two objects
3 marks7
Calculate the momentum of each object.
Compare the two values.
State a conclusion.
Example. A bowling ball of mass 6.0 kg rolls at 3.0 m/s. A football of mass 0.45 kg is kicked at 30 m/s. Which has more momentum? Show your working.
Show the model answer
bowling ball: p = 6.0 × 3.0 = 18 kg m/s (1) football: p = 0.45 × 30 = 13.5 kg m/s (1) The bowling ball has more momentum (1).
Calculate a change in momentum with a change of direction
3 marks8
Choose a positive direction.
Calculate the initial and final momentum with signs.
Change = final − initial; give the size and direction.
Example. A 0.40 kg ball moving at 5.0 m/s to the right hits a wall and rebounds at 3.0 m/s to the left. Calculate the change in momentum of the ball.
Show the model answer
taking right as positive: initial p = +2.0 kg m/s and final p = 0.40 × (−3.0) = −1.2 kg m/s (1) change = −1.2 − (+2.0) (1) = −3.2 kg m/s, i.e. 3.2 kg m/s to the left (1)
Shortcuts and memory tricks
Momentum is 'mass in motion': no motion, no momentum.
Grams to kilograms first: divide by 1000.
For a rebound, add the sizes of the two momenta to get the size of the change (2.0 + 1.2 = 3.2 kg m/s).
Where marks are lost
Using a mass in grams.
Ignoring direction: for a rebound, subtracting the speeds instead of taking the directions into account.
Writing the unit as kg/m s or kg/ms. It is kg m/s.
Confusing momentum (m v) with kinetic energy (½ m v2).
Exam technique
p = m v must be recalled (Higher tier).
In any question with directions, state which direction you are taking as positive at the start.
Show the momentum of each object separately before combining them.
Quick recall
Cover the answers and test yourself. The app has these as flashcards that come back just before you'd forget them.
A cricket ball has a mass of 0.16 kg and travels at 25 m/s. Calculate the momentum of the ball. Use the equation: momentum = mass × velocity
4.0 kg m/s
Write down the equation that links mass (m), momentum (p) and velocity (v).
p = m v
A shopping trolley of mass 18 kg moves at 1.2 m/s. Calculate its momentum. Use the equation: momentum = mass × velocity
21.6 kg m/s
Sample questions
Written for this site in the style of AQA exam questions. They are not taken from real past papers.
Question 1Easy4 marks
(a) A cricket ball has a mass of 0.16 kg and travels at 25 m/s. Calculate the momentum of the ball. Use the equation: momentum = mass × velocity[2]
(b) What is the unit of momentum? Tick (✓) one box.[1]
kg m/s
kg m/s2
N/m
J/s
(c) Momentum is a vector quantity. What does this mean?[1]
Show the answer and mark scheme
(a)Answer: 4.0 kg m/s
p = 0.16 × 25
4.0 (kg m/s)
(b)Answer: kg m/s
(c)Answer: It has magnitude and direction.
it has both magnitude (size) and direction
Question 2Medium5 marks
(a) Write down the equation that links mass (m), momentum (p) and velocity (v).[1]
(b) A car of mass 1200 kg travels at 15 m/s. Calculate the momentum of the car.[2]
(c) A lorry of mass 9000 kg has the same momentum as the car. Calculate the velocity of the lorry.[2]
Show the answer and mark scheme
(a)Answer: p = m v
p = m v / momentum = mass × velocity
(b)Answer: 18 000 kg m/s
p = 1200 × 15
18 000 (kg m/s)
(c)Answer: 2.0 m/s
18 000 = 9000 × v
v = 2.0 (m/s)
Question 3Hard7 marks
A tennis ball of mass 0.058 kg and a bowling ball of mass 6.0 kg each have a momentum of 3.0 kg m/s.
(a) Calculate the velocity of the tennis ball.[2]
(b) Calculate the velocity of the bowling ball.[1]
(c) Calculate the kinetic energy of the tennis ball.[1]
(d) Calculate the kinetic energy of the bowling ball.[1]
(e) A student says: ‘Objects with the same momentum must have the same kinetic energy.’ Use your answers to explain why the student is wrong.[2]
Show the answer and mark scheme
(a)Answer: 52 m/s (51.7 m/s) m/s
v = 3.0 ÷ 0.058
52 (m/s)
(b)Answer: 0.50 m/s
3.0 ÷ 6.0 = 0.50 (m/s)
(c)Answer: 78 J (77.6 J) J
0.5 × 0.058 × 51.72 = 78 (J)
(d)Answer: 0.75 J
0.5 × 6.0 × 0.502 = 0.75 (J)
(e)Answer: The tennis ball has about 100 times more kinetic energy: for equal momentum, the lighter, faster object has more kinetic energy because KE depends on v².
the tennis ball has about 100 times as much kinetic energy as the bowling ball, even though their momenta are equal
kinetic energy depends on (speed)2, so for the same momentum the object with the smaller mass (and greater speed) has more kinetic energy