Question

A merry-go-round accelerates from rest to 0.74 rad/s in 34 s.

Part A

Assuming the merry-go-round is a uniform disk of radius 8.0 m and mass 3.20×10⁴ kg , calculate the net torque required to accelerate it.

Express your answer to two significant figures and include the appropriate units

Answer 1

Initial angular speed of the merry-go-round = ₁ = 0 rad/s (At rest)

Angular speed of the merry-go-round after 34 sec = ₂ = 0.74 rad/s

Time period = T = 34 sec

Angular acceleration of the merry-go-round =

₂ = ₁ + T

0.74 = 0 + (34)

= 2.176 x 10^-2 rad/s²

Mass of the merry-go-round = M = 3.2 x 10⁴ kg

Radius of the merry-go-round = R = 8 m

Moment of inertia of the merry-go-round = I

I = MR²/2

I = (3.2x10⁴)(8)²/2

I = 1.024 x 10⁶ kg.m²

Net torque on the merry-go-round =

= I

= (1.024x10⁶)(2.176x10^-2)

= 2.2 x 10⁴ N.m

A) Net torque required to accelerate the merry-go-round = 2.2 x 10⁴ N.m