Rotational Motion: Diagram-Based Questions (1)

Question

A uniform solid disc of mass $M = 2$ kg and radius $R = 0.5$ m rotates about its central axis. A force $F = 10$ N is applied tangentially to the rim. Find the angular acceleration of the disc.

Solution — Step by Step

Why This Works

The equation $\tau = I \alpha$ is the rotational version of $F = ma$. The moment of inertia plays the role of mass — it measures how hard it is to angularly accelerate the body. The torque is the rotational analogue of force.

For a tangential force, the torque is simply $F R$. If the force were applied at angle $\theta$ to the radius vector, we’d use $\tau = F R \sin\theta$.

Alternative Method

Use energy methods if the question asks for angular velocity after rotation through an angle $\phi$: work done by torque $= \tau \phi$ equals change in rotational KE $\frac{1}{2} I \omega^2$. For pure angular acceleration, the direct $\tau = I \alpha$ approach is faster.

Common Mistake

Students sometimes use $I = MR^2$ (ring formula) for a disc. The factor of $\frac{1}{2}$ matters — using the wrong formula doubles your answer. Always pause and ask: solid or hollow? Disc or ring? The shape determines the constant.