A disc at rest is subjected to a uniform angular acceleration about its axis. Let $ heta$ and $ heta^1$ be the angle made by the disc in $2^{ ext {nd }}$ and $3^{ ext {rd }}$ second of its motion. The ratio $\frac{ heta}{ heta^1}$ is

Question

A disc at rest is subjected to a uniform angular acceleration about its axis. Let $	heta$ and $	heta^1$ be the angle made by the disc in $2^{	ext {nd }}$ and $3^{	ext {rd }}$ second of its motion. The ratio $\frac{	heta}{	heta^1}$ is

Aicharya · Accepted Answer

Kinematic equation for rotational motion, $\theta=\omega_0 t+\frac{1}{2} \alpha t^2$
Disk is initially at rest, $\omega_0=0$ $\Rightarrow \theta=\frac{1}{2} \alpha t^2...(i)$ Angle described in $2^{\text {nd }}$ second is, $\theta_1=\frac{1}{2} \alpha(2)^2=2 \alpha$
Angle described in first 3 seconds will be, $\theta_2=\frac{1}{2} \alpha(3)^2=4.5 \alpha$
Angle described in $3^{\text {rd }}$ second will be, $\theta^{\prime}=\theta_2-\theta_1$ $\begin{aligned} & =4.5 \alpha-2 \alpha=2.5 \alpha \\ \therefore \quad & \frac{\theta}{\theta^{\prime}} \end{aligned}=\frac{2}{2.5}=\frac{4}{5}$ .

A disc at rest is subjected to a uniform angular acceleration about its axis. Let $\theta$ and $\theta^1$ be…

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