Question

A block hangs from a string wrapped on a disc of radius $20\text{cm}$ free to rotate about its axis which is fixed in a horizontal position. If the angular speed of the disc is $10\text{rad/s}$ at some instant, with what speed is the block going down at that instant? (Answer in $\text{m/s}$)

Answer 1

Given, angular speed of disc $\omega =10\text{rad/s}$
Radius of the ring $r=20\text{cm}$
$r=0.2\text{m}$
As we know, $v=\omega r$ is the velocity of a point on the the outer edge of the disc.
$v=10\text{(rad/s)}\times 0.2\text{(m)}$
$v=2\text{m/s}$
which will be the same as the velocity of the string and the block.