Question

A 110-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.600 rev/s in 2.00 s

Answer 1

155 N

Step-by-step explanation:

We are given following data for a uniform, solid, horizontal disk:

r = 1.5 m

m= 110 kg

t=2 s

w = 0.6

Torque is given by:

т = F*r

=I*α

Solving it for the force exerted on the rope:

F = I*α/r

= (1/2*m*r^2)*(2π*w/t )/r

= (1/2*110*1.5^2)*(2π*0.6/2 )/1.5

= 155 N