Question

A 30kg uniform solid cylinder has a radius of 0.18m. if the cylinder accelerates at 0.023 rad/s^2 as it rotates about an axis through its center, how large is the torque acting on the cylinder? With work please

Answer 1

Answer:

0.011 N-m

Explanation:

Given that

The mass of a solid cylinder, m = 30 kg

The radius of the cylinder, r = 0.18 m

The acceleration of the cylinder, $\alpha =0.023\ rad/s^2$

It rotates about an axis through its center. We need to find the torque acting on the cylinder. The formula for the torque is given by :

$\tau=I\alpha$

Where

I is the moment of inertia of the cylinder,

For cylinder,

$I=\dfrac{mr^2}{2}$

So,

$\tau=\dfrac{mr^2\alpha }{2}\\\\\tau=\dfrac{30\times (0.18)^2\times 0.023 }{2}\\\\\tau=0.011\ N-m$

So, the required torque on the cylinder is 0.011 N-m.