Question

A wheel starts rotating from rest at time $t=0$ with a angular acceleration of $50radians/s^2$. The angular acceleration $\left(\alpha \right)$ decreases to zero value after $5$ seconds. During this interval, $\alpha$ varies according to the question
$\alpha ={\alpha }_0(1-\frac{t}{5})$
The angular velocity at $T=5s$ will be

• A. $10rad/s$
• B. $250rad/s$
• C. $125rad/s$
• D. $100rad/s$

Answer 1

Answer: (C)

$125rad/s$

$\alpha ={\alpha }_0(1-\frac{t}{5})$
At $t=0,\alpha ={\alpha }_0\therefore {\alpha }_0=50rad/s^2$
$\frac{d\omega }{dt}={\alpha }_0(1-\frac{t}{5})$
$\therefore {\int }_0^{\omega }d\omega ={\alpha }_0{\int }_0^5(1-\frac{t}{5})dt\Rightarrow \omega ={\alpha }_0{[t-\frac{t^2}{10}]}_0^5$
$=50(5-\frac{25}{10})rad/s=125rad/s$.