Question

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

• A. $\frac{\pi}{25}$rev/ sec
• B. $\frac{1}{\pi}$rev/sec
• C. $\frac{25}{\pi}$rev/sec
• D. None of these

Answer 1

Answer: (C)

$\frac{25}{\pi}$rev/sec

Answer 2

$\omega_{1} = 0,$ $\omega_{2} = 20rad/sec,t = 5sec ⥂$

$\alpha = \frac{\omega_{2} - \omega_{1}}{t} = \frac{20 - 0}{5} = 4rad/sec^{2}$From the equation $\theta = \omega_{1}t + \frac{1}{2}\alpha t^{2} = 0 + \frac{1}{2}(4).(5)^{2} = 50rad$

$2\pi rad$means 1 revolution.

$\therefore$ 50 Radian means $\frac{50}{2\pi}$or $\frac{25}{\pi}$rev.