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Angular impulse
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Torque integrated over time changes angular momentum.
∫τ dt = ΔLThe time integral of torque ∫τ dt changes angular momentum, the rotational version of impulse.
A 5 N·m torque for 2 s adds 10 kg·m²/s.
Use same axis for torque and L.
In more detail
Angular impulse is the torque multiplied by the time it acts, and it equals the change in angular momentum. It is the rotational version of linear impulse.
Real-world uses
- A golf club's contact time with the ball sets the angular impulse on the ball.
- Spinning a wheel by applying a torque for a short time.
- A short torque pulse applied to a spinning shaft changes its angular momentum by the area under the torque-time graph.
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Frequently asked questions
What are the units?
Newton metre seconds, equal to kilogram metres squared per second.
Is it the same as torque?
No. Torque is a rate, while angular impulse is the torque multiplied by time.
Is angular impulse the same as the angular momentum change?
Yes. Integrating the torque over time gives the change in angular momentum, just as linear impulse gives change in linear momentum.
Related topics in Rotational Motion
Pulley with mass · Atwood with real pulley · Yo-yo and unwinding cylinder · Static friction in rolling · Slipping to rolling transition · Bohr angular momentum