Question

A wheel having a radius of $10cm$ is coupled by a belt to another wheel of radius $30cm$. 1st wheel increases its angular speed from rest at a uniform rate of 1.57 $rad/s^2$. The time for the 2nd wheel to reach a rotational speed of $100rev/min$ is (assume that the belt does not slip):

• A. $20s$
• B. $10s$
• C. $1.5s$
• D. $15s$

Answer 1

Answer: (A)

$20s$

${\alpha }_1=1.57rad/s^2$
${\omega }_2=100rev/m$
$=100\times \frac{2\pi }{60}$
$=\frac{10\pi }{3}rad/s$
linear velocity of belt is equal
$\therefore {\omega }_1{r}_1={\omega }_2{r}_2$ and ${\alpha }_1{r}_1={\alpha }_2{r}_2$
$\therefore {\alpha }_2=\left(1.57\right)\left(\frac{10}{30}\right)$
$=\frac{1.57}{3}rad/s^2$
$\omega ={\omega }_0+\alpha t$
$\frac{10\pi }{3}=0+\frac{1.57}{3}\times t$
$t=20s$