Question

A wheel has radius $30$ cm. The wheel starts from rest and attains a speed of $300$ r.p.m. in $3$ minutes. What is its angular acceleration? What is angular displacement within this time?

Answer 1

Angular displacement Avg Angular Velocity time

Initial Angular Velocity $\left({\omega }_o\right)=0$

Final Angular Velocity $\left({\omega }_f\right)=\frac{2\pi N}{60}$

$=2\times \frac{3.14}{60}\times 300$

$=31.4rad/s$

Avg. Angular Velocity $\left(\omega \right)=\frac{{\omega }_o+{\omega }_f}{2}$

$\omega =0+\frac{31.4}{2}=15.7rad/s$

Angular displacement $\theta =\omega t$

$=15.7\times 3\times 60$

$\theta =2826rad$

Angular Acceleration $\left(\alpha \right)=\frac{{\omega }_f-{\omega }_o}{t}=\frac{15.7-0}{180}$

$\alpha =0.087rad/s^2$