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 7.0 s . Consider the merry-go-round to be a uniform disk of radius 6.0 m and mass 25,000 kg. Suppose that it is supported by bearings that produce negligible friction torque.

Answer 1

Answer

given,

initial speed of merry-go-round = 0 rad/s

final speed of merry-go-round = 1.5 rad/s

time = 7 s

Radius of the disk = 6 m

Mass of the merry-go-round = 25000 Kg

Moment of inertia of the disk

$I = \dfrac{1}{2}MR^2$

$I = \dfrac{1}{2}\times 25000\times 6^2$

   I = 450000 kg.m²

angular acceleration

$\alpha = \dfrac{\omega_f-\omega_0}{t}$

$\alpha = \dfrac{1.5-0}{7}$

$\alpha =0.214\ rad/s^2$

we know,

$\tau= I \alpha$

$\tau= 450000\times 0.214$

$\tau=96300\ N.m$