Question

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

• A. $20\text{s}$
• B. $0\text{s}$
• C. $1.5\text{s}$
• D. $15\text{s}$

Answer 1

The correct option is A $20\text{s}$

${\alpha }_1=1.57rad/s^2$
${\omega }_2=100rev/m$
$=100\times \frac{2\pi }{60}$
$=\frac{10\pi }{3}rad/s$
linear velocity of belt is equal
$\therefore {\omega }_1{r}_1={\omega }_2{r}_2$ and $a_1{r}_1={\alpha }_2{r}_2$
$\therefore {\alpha }_2=\left(1.57\right)\left(\frac{10}{30}\right)$
$=\frac{1.57}{3}rad/s^2$
$\omega ={\omega }_0+\alpha t$
$\frac{10\pi }{3}=0+\frac{1.57}{3}\times t$
$t=20s$