A stationary merry-go-round of radius 8 feet is started in motion by a push consisting of a force of 7 pounds on the outside edge, tangent to the circular edge of the merry-go-round, for 4 seconds. The moment of inertia of the merry-go-round is . Find the resulting angular velocity of the merry-go-around.
A) 2 rad/sec
B) 8 rad/sec
C) 1 rad/sec
D) 7 rad/sec

Question

A stationary merry-go-round of radius 8 feet is started in motion by a push consisting of a force of 7 pounds on the outside edge, tangent to the circular edge of the merry-go-round, for 4 seconds. The moment of inertia of the merry-go-round is  . Find the resulting angular velocity of the merry-go-around.
A) 2 rad/sec 
B) 8 rad/sec 
C) 1 rad/sec 
D) 7 rad/sec

Quizplus · Accepted Answer

The torque applied by the force is given by:
τ = F * r
where F is the force applied and r is the radius of the merry-go-round.
τ = 7 * 8 = 56 lb-ft
Using the formula for torque:
τ = I * α
where I is the moment of inertia and α is the angular acceleration. Solving for α, we get:
α = τ / I
α = 56 / 11eaa88b_9374_d835_a696_eb4e827623e7_TB5869_11 = 5.0909 rad/sec²
The final angular velocity is given by:
ω = α * t
where t is the time the force is applied. Plugging in the values, we get:
ω = 5.0909 * 4 = 20.364 rad/sec
However, the question asks for the resulting angular velocity, not the final one. Since the merry-go-round starts from rest, the initial angular velocity is 0. Therefore, the resulting angular velocity is 20.364 rad/sec, which is closest to choice B) 8 rad/sec.

A Stationary Merry-Go-Round of Radius 8 Feet Is Started in Motion