Question

A mechanic needs to replace the motor for a merry-go-round. The merry-go-round should accelerate from rest to 1.5 rad/s in 6.0s . Consider the merry-go-round to be a uniform disk of radius 5.5m and mass 29,000 kg. Suppose that it is supported by bearings that produce negligible friction torque.What torque specifications must the new motor satisfy?

Answer 1

109656.25 Nm

Step-by-step explanation:

`\omega_f` = Final angular velocity = 1.5 rad/s

`\omega_i` = Initial angular velocity = 0

`\alpha` = Angular acceleration

t = Time taken = 6 s

m = Mass of disk = 29000 kg

r = Radius = 5.5 m

`\omega_f=\omega_i+\alpha t\\\Rightarrow \alpha=(\omega_f-\omega_i)/(t)\\\Rightarrow \alpha=(1.5-0)/(6)\\\Rightarrow \alpha=0.25\ rad/s^2`

Torque is given by

`\tau=I\alpha\\\Rightarrow \tau=(1)/(2)mr^2\alpha\\\Rightarrow \tau=(1)/(2)29000* 5.5^2* 0.25\\\Rightarrow \tau=109656.25\ Nm`

The torque specifications must be 109656.25 Nm