Question

A rotating wheel changes angular speed from 1800 rpm to 3000 rpm in 20 s. What is the angular acceleration assuming to be uniform?

• A. $60\pi$ rad $s^{-2}$
• B. $90\pi$ rad $s^{-2}$
• C. $2\pi$ rad $s^{-2}$
• D. $40\pi$ rad $s^{-2}$

Answer 1

Answer: (C)

$2\pi$ rad $s^{-2}$

Initial frequency of rotation ${\nu }_i=1800$ rpm $=1800/60=30$ rps

Thus initial angular frequency $w_i=2\pi {\nu }_i=60\pi$ $rad/s$

Final frequency of rotation ${\nu }_f=3000$ rpm $=3000/60=50$ rps

Thus final angular frequency $w_f=2\pi {\nu }_f=100\pi$ $rad/s$

$\therefore$ Angular acceleration $\alpha =\frac{w_f-w_i}{t}$

OR $\alpha =\frac{100\pi -60\pi }{20}=2\pi$ $rad/s^2$