Question

A grinding wheel attained a velocity of $20rad/sec$ in $5sec$ starting from rest. Find the number of revolutions made by the wheel.

• A. $\frac{\pi }{25}$ revolution per sec
• B. $\frac{1}{\pi }$ revolution per sec
• C. $\frac{25}{\pi }$ revolution
• D. $None$

Answer 1

The correct option is C $\frac{25}{\pi }$ revolution

The angular acceleration given as,

$a=\frac{{\omega }_f-w_i}{t}$

$a=\frac{20-0}{5}=4rad/s^2$

By using

$\theta ={\omega }_{i}t+\frac{1}{2}a{t}^2$

$\theta =0+0.5\times 4\times 25$

$\theta =50rad$

Number of revolution is

$n=\frac{50}{2\pi }=\frac{25}{\pi }$

Hence, the number of revolution is $\frac{25}{\pi }$.