Question

A $4.00-m$ length of light nylon cord is wound around a uniform cylindrical spool of radius $0.500m$ and mass $1.00kg$. The spool is mounted on a frictionless axle and is initially at rest. The cord is pulled from the spool with a constant acceleration of magnitude $2.50m/s^2$.
How long does it takes the spool to reach this angular speed?

Answer 1

Given,

Length of nylon rod is $4m$

radius is $0.5m$

mass is $1kg$

acceleration is $2.5m/s^2$

Angular velocity is $8rad/s$

We know that

$V=\omega r$

Here,

$V$ is velocity

$\omega$ is angular velocity

$r$ is radius

Now,

$at=\omega rt=\frac{\omega r}{a}$

substitute all value in above equation

$t=\frac{0.5\omega }{2.5}t=\frac{8}{5}=1.6s$