Question

On applying brakes the angular velocity of a flywheel reduces from $900$ cycles/min to $720$ cycles/min in $6$ seconds. Its angular retardation in rad$/s^2$ will be?

• A. $\pi /3$
• B. $\pi$
• C. $2\pi /3$
• D. $2\pi$

Answer 1

The correct option is B $\pi$

for one complete cycle, the angular displacement is $2\pi$ so, now we will convert the angular speeds from cycles/minute units to rad/sec.

$1cycle/minute=\frac{2\pi rad}{60sec}$

so, $900cycles/minute=\frac{2\pi rad}{60sec}\times 900$

$900cycles/minute=30\pi rad/sec$

similarly,

$720cycles/minute=24\pi rad/sec$

The expression for angular acceleration is as follows:

$\alpha =\frac{{\omega }_f-{\omega }_i}{△t}$

$\alpha =\frac{30\pi rad/sec-24\pi rad/sec}{6sec}$

$\alpha =\pi rad/se{c}^2$

so, the answer is $\pi$