Rotational second law
Net torque equals moment of inertia times angular acceleration, tau = I alpha. It is F = ma for spinning.
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Analogy
The same push has less effect on a heavier flywheel.
Example
I = 1/2 M R^2 = 0.5 kg m^2alpha = tau / Ialpha = 2 / 0.5 = 4 rad/s^2
In practice
A 4 kg, 0.5 m radius solid disk with 2 N m of torque speeds up at 4 rad/s squared.
Practice
Flashcards
- State the rotational form of Newton's second law.Net torque = I x alpha.
Questions people ask
How is tau = I alpha like F = ma?
They are the same idea. Torque plays the role of force, moment of inertia plays the role of mass, and angular acceleration plays the role of linear acceleration. The same push-gives-acceleration logic applies, so problem methods carry over to spinning objects.
How do I solve a pulley with a hanging mass?
Write F = ma for the hanging mass, with tension and weight. Write tau = I alpha for the pulley, using tension times radius. Link them with a = alpha R if the rope does not slip. Then solve the two equations for the tension and acceleration.