Impulse-Momentum Theorem
Relating impulse to the change in linear momentum of an object (J = Δp).
What is Impulse-Momentum Theorem?
The product of the average force acting on an object and the time interval over which the force acts. It is a measure of the effect of a force acting over a period of time.
Key formula / rule: Impulse
Key points
- Define impulse and its relationship to force and time.
- State and explain the Impulse-Momentum Theorem.
- Calculate impulse given force and time, or change in momentum.
- Apply the theorem to solve problems involving collisions and impacts.
Common exam trap
Confusing impulse with momentum.
Definitions
- Term
Impulse
- Meaning
The product of the average force acting on an object and the time interval over which the force acts. It is a measure of the effect of a force acting over a period of time.
- Term
Linear Momentum
- Meaning
The product of an object's mass and its velocity. It is a measure of an object's motion and is a vector quantity.
Learning objectives
Define impulse and its relationship to force and time.
State and explain the Impulse-Momentum Theorem.
Calculate impulse given force and time, or change in momentum.
Apply the theorem to solve problems involving collisions and impacts.
Formulae
- Name
Impulse
- Note
J is impulse, Favg is average force, \Δ t is time interval.
- Expression
J = Favg \Δ t
- Name
Change in Linear Momentum
- Note
\Δ p is change in momentum, pf is final momentum, pi is initial momentum, m is mass, vf is final velocity, vi is initial velocity.
- Expression
\Δ p = pf - pi = mvf - mvi
- Name
Impulse-Momentum Theorem
- Note
Equates impulse to the change in linear momentum.
- Expression
J = \Δ p \implies Favg \Δ t = mvf - mvi
Prerequisites
Understanding of Force and Newton's Laws of Motion
Concept of Velocity and Acceleration
Definition of Mass
Understanding of Linear Momentum
Common mistakes
Confusing impulse with momentum.
Forgetting that impulse and momentum are vector quantities and not considering direction.
Using the instantaneous force instead of the average force in calculations.
Incorrectly calculating the change in momentum (e.g., not subtracting initial from final momentum).
Keywords
Impulse
Momentum
Impulse-Momentum Theorem
Force
Time Interval
Change in Momentum
Collision
Impact
Newton's Second Law
Practice preview
A body of mass m is moving with velocity v. If a force F acts on it for time Δt, the change in momentum is:…
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A ball of mass 0.5 kg moving with a velocity of 10 m/s collides with a wall and rebounds with a velocity of 8 m/s. The impulse experienced by the ball during the collision is:…
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A body of mass 5 kg is subjected to a force that varies with time as shown in the graph. What is the impulse imparted to the body during the time interval from t = 0 to t = 4 s?…
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