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Torque and angular momentum
Intermediate
Net torque equals the rate of change of L.
τ = dL/dtτ_net = dL/dt. It is the rotational form of Newton's second law and also covers changing I.
A constant 2 N·m torque for 5 s adds 10 kg·m²/s.
Use the same origin for τ and L.
In more detail
The rate of change of angular momentum equals the net external torque, τ = dL/dt. This is the rotational version of Newton's second law in momentum form.
Real-world uses
- Engineers use torque and angular momentum to design turbines and motors.
- Satellite attitude control uses reaction wheels that change angular momentum.
- Engineers analyse the spin of a turbine by relating the net torque on it to the rate of change of its angular momentum.
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Frequently asked questions
What if the net torque is zero?
Then the angular momentum stays constant.
Is this valid for systems of particles?
Yes, using the total angular momentum of the system.
Is this the same as the rotational form of Newton's second law?
Yes, it is the general form. For a fixed axis, it reduces to torque equals I times angular acceleration.
Related topics in Rotational Motion
Work and power in rotation · Angular momentum of a particle · Angular momentum of rigid body · Conservation of angular momentum · Spinning skater and diver · Collisions in rotation