Question

A constant torque of 23 N-m is applied to a shaft that is rotating with a CW angular velocity of 22.6 rad/s. Determine the time required to reverse the direction of motion and achieve a CCW rotation of 22.6 rad/s.

Answer 1

2.78 s

Step-by-step explanation:

We are given that

Torque,
`\tau=23 Nm`

Initial angular velocity,
`\omega_0=22.6 rad/s`

Final angular velocity,
`\omega=-22.6 rad/s`

Mass,m=2 kg

R=0.53 m

r=0.27 m

Moment of inertia of system=
`I=2m(R^2+r^2)`

`I=2* 2((0.53)^2+(0.27)^2}=1.4152 kgm^2`

Angular acceleration,
`\alpha=-(\tau)/(I)=-(23)/(1.4152)=-16.25rad/s^2`

`\alpha=(\omega-\omega_0)/(t)`

`t=(\omega-\omega_0)/(\alpha)`

`t=(-22.6-22.6)/(-16.25)=2.78 s`