A metal coin of mass 5 g and radius 1 cm is fixed to a thin stick AB of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about AB at 25 rotations per second in 5 s, is close to:

 Step 1: Angular acceleration

Initial angular velocity ω0=0

ω=25 rps=25×2π=50π rad/s

$$α=\ \frac{\ ω\ −\ ω_0}{t-0}​​=\ \frac{\ 50\pi}{5}​=10\pi rad/s2$$

 Step 2: Moment of inertia

For a disc about diameter (axis AB):

Given:

$$m=5\times10^{-3}kg,\ R=10^{-2}m$$

$$I=\ \frac{\ 1}{4}\cdot​(5\times10^{-3})(10^{-2})^2$$

 Step 3: Torque

$$τ=Iα$$

$$τ=\ \frac{\ 1}{4}​(5\times10^{-3})(10^{-2})⋅10\pi$$

$$τ\approx2.0\times10^{-5}Nm$$