Question

g A wheel of rotational inertia 16 kg·m2 is subjected to a net torque of 24 N·m. The wheel starts at rest. After the torque has acted for 5.0 s, at what rate is work being done by the torque?

Answer 1

P = 180 watts

Step-by-step explanation:

It is given that,

Inertia of the wheel,
`I=16\ kgm^2`

Net torque acting on the wheel,
`\tau=24\ Nm`

Initial speed of the wheel,
`\omega_i=0`

Time, t = 5 s

We know that the relation between the torque and the angular acceleration is given by :

`\tau=I\alpha`

`\alpha` is the angular acceleration

`\alpha =(\tau)/(I)`

`\alpha =(24\ Nm)/(16\ kgm^2)`

`\alpha =1.5\ rad/s^2`

Using first equation of rotational kinematics as :

`\omega_f=\omega_i+\alpha t`

`\omega_f=1.5* 5`

`\omega_f=7.5\ rad/s`

We know that the rate at which the work is done by the torque is called the power of any object. Its formula in rotational motion is given by :

`P=\tau * \omega_f`

`P=24\ Nm* 7.5\ rad/s`

P = 180 watts

So, the power of the wheel is 180 watts. Hence, this is the required solution.