Problem — Given α, find the torque

Problem

A disc of $I = 0{,}05\;\mathrm{kg\,m^2}$ reaches $\omega = 60\;\mathrm{rad/s}$ in $3\;\mathrm{s}$, starting from rest. Calculate the net torque applied.

Solution

First the angular acceleration, from the definition $\alpha = \Delta\omega/\Delta t$: $\alpha = \frac{60 - 0}{3} = 20\;\mathrm{rad/s^2}$ Then the torque, from the second law of rotation $\tau = I\alpha$: $\tau = I\,\alpha = 0{,}05\cdot 20 = \ev{1{,}0\;\mathrm{N\,m}}$ This is the inverse problem of rotational dynamics: from the effect (the observed acceleration) one works back to the cause (the applied torque).

Links

Topics: Rotational dynamics Concepts: Angular acceleration · Torque Objects: Rotating disc