Question

A wheel having a diameter of $3m$ starts from rest and accelerates uniformly to an angular velocity of $210r.p.m$. in $5$ seconds. Angular acceleration of the wheel is

• A. $4.4\pi \frac{rad}{s^2}$
• B. $3.3\pi \frac{rad}{s^2}$
• C. $2.2\pi \frac{rad}{s^2}$
• D. $1.1\pi \frac{rad}{s^2}$

Answer 1

The correct option is A $4.4\pi \frac{rad}{s^2}$

Initial angular velocity,$\omega 0=0$

Final angular velocity, $\omega 0=210rpm$

$=210\times \frac{2\Pi }{60}rad/sec$

$=210\times 2\times \frac{22}{7\times 60}$

$=22rad/sec$

Use formula,$\omega ={\omega }_0+\alpha t$

$22=0+\alpha \times 5$

$alpha=\frac{22}{5}=4.4\frac{rad}{s^2}$