Question

A particle having angular velocity $10rad/sec$ and angular acceleration of $5rad/se{c}^2$ for $10sec$. Find the number of rotations performed by the particle in $10sec$.

• A. $55$
• B. $75$
• C. $125$
• D. $150$

Answer 1

The correct option is A $55$

From rotational kinematics:

$\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$

where $\theta$ is angular displacement

${\omega }_0$ is angular velocity

$\alpha$ is angular acceleration

and $t$ is time

$\therefore \theta =10\times 10+\frac{1}{2}\times 5\times 100=100+250=350rad$

To get no. of rotations performed we divide $\theta$ by $2\pi$

$\frac{\theta }{2\pi }=\frac{350}{2\pi }\cong 55$