Physics overview
What is angular impulse?
Angular impulse describes the effect of torque acting over a time interval. It equals the resulting change in angular momentum.
Formula
Angular impulse formula
Angular ImpulseJ = τt = ΔL
- J is angular impulse in N·m·s.
- τ is torque in N·m.
- t is time in seconds.
- ΔL is the change in angular momentum.
Worked example
A torque of 8 N·m acts for 3 seconds
- Write the formula: J = τt.
- Substitute the values: J = 8 × 3.
- Calculate angular impulse: J = 24 N·m·s.
Rearranged equations
Solve for torque or time
Torque
τ = J ÷ t
Divide angular impulse by time.
Time
t = J ÷ τ
Divide angular impulse by torque.
Angular momentum relationship
Angular impulse equals ΔL
The angular impulse applied to an object equals its change in angular momentum. A larger torque or a longer application time produces a larger rotational momentum change.
Units
Standard SI units
Use newton meter seconds for angular impulse, newton meters for torque, and seconds for time.
Real-world applications
Where angular impulse is used
- Starting and stopping rotating machinery.
- Applying torque to wheels and flywheels.
- Sports involving rotational motion.
- Motor and turbine performance analysis.
- Studying changes in angular momentum.
Calculation limits
Important assumptions
- All entered values must be greater than zero.
- Torque is treated as constant during the time interval.
- The torque direction is not represented.
- Units are not converted automatically.
Related tools
Continue your rotational analysis
Use the Torque Calculator to calculate torque, force, or lever arm distance.
Use the Angular Momentum Calculator to calculate angular momentum, moment of inertia, or angular velocity.
Questions and answers
Angular impulse calculator FAQ
What formula does the angular impulse calculator use?
It uses J = τt = ΔL, where angular impulse equals torque multiplied by time and also equals the change in angular momentum.
What is angular impulse?
Angular impulse measures the rotational effect of torque acting over a time interval.
How do you calculate torque from angular impulse?
Divide angular impulse by time using τ = J ÷ t.
What units are used for angular impulse?
Angular impulse is measured in newton meter seconds, written as N·m·s.