Question 227: Work, Energy and Power & Circular Motion

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

Accepted Answer

Kinematic equation for rotational motion,
$$	heta=\omega_0 t+\frac{1}{2} \alpha t^2$$
Disk is initially at rest, $\omega_0=0$
$$\Rightarrow 	heta=\frac{1}{2} \alpha t^2
\quad	ext{.... (i)}$$
Angle described in $2^{	ext {nd }}$ second is,
$$	heta_1=\frac{1}{2} \alpha(2)^2=2 \alpha\quad 	ext{... [From (i)]}$$
Angle described in first 3 seconds will be,
$$	heta_2=\frac{1}{2} \alpha(3)^2=4.5 \alpha\quad	ext{.... [From (i)]}$$
Angle described in $3^{	ext {rd }}$ second will be,
$$\begin{aligned}
	heta^{\prime} & =	heta_2-	heta_1 \
& =4.5 \alpha-2 \alpha=2.5 \alpha
\end{aligned}$$
$$	herefore \quad \frac{	heta}{	heta^{\prime}}=\frac{2}{2.5}=\frac{4}{5}$$

Answer

$2: 3$

Answer

$1: 2$

Answer

$2: 3$

Answer

$4: 5$

Work, Energy and Power & Circular Motion

A disc at rest is subjected to a uniform angular acceleration about its axis. Let \theta and \theta_1 be the angle made by the disc in 2^{\text {nd }} and 3^{\text {rd }} second of its motion. The ratio \frac{\theta}{\theta_1} is

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