Question

Physics. All the answers I get are wrong. Need help

Answer 1

The torque is given by:

`\tau=I\alpha`

where I is the moment of inertia of the disk and alpha is the angular acceleration.

The moment of inertia for a disk is given by:

`I=(1)/(2)mr^2`

where m is the mass and r is the radius. The angular acceleration can be obtained from the relation:

`\alpha=(\omega^2_f-\omega^2_i)/(2\theta)`

In this case the mass is 0.240 kg and the radius is 15.25 cm or 0.1525 meters. Furthermore, the initial angular velocity is zero, the final angular velocity is 3.49 rad/s and the angle it takes to reach it is 1.2 by 2pi. Plugging this in the equation for the torque we have:

`\begin{gathered} \tau=((0.240\cdot0.1525^2)/(2))((3.49^2-0^2)/(2(1.2\cdot2\pi))) \\ \tau=2.0663*10^(-3) \end{gathered}`

Therefore the torque the motor must deliver is:

`2.0663*10^(-3)\text{ Nm}`