Question

Sanjay and Ting, each with a mass of 25 kg, are riding opposite each other on the edge of a 150 kg, 3.0-m-diameter playground merry-go-round that's rotating at 15 rpm. Each walks straight inward and stops 35 cm from the center.

What is the new angular velocity, in rpm?
Express your answer in revolutions per minute.

Answer 1

To find the new angular velocity, we can use the principle of conservation of angular momentum. By applying the formula for angular momentum and simplifying, we can determine the final angular velocity of the merry-go-round after the riders move closer to the center.

Step-by-step explanation:

To solve this problem, we need to apply the principle of conservation of angular momentum. The initial total angular momentum of the merry-go-round and the two riders is equal to the final total angular momentum after the riders move closer to the center. The initial angular momentum can be calculated using the formula L = Iω, where I is the moment of inertia and ω is the angular velocity. Since the merry-go-round and the two riders are initially at rest, their initial angular momentum is zero. Therefore, the final angular momentum must also be zero.

The moment of inertia of the merry-go-round is given by I = MR², where M is the mass of the merry-go-round and R is its radius.

Let's calculate the initial and final angular velocities:

1. Step 1: Calculate the initial moment of inertia (Iinitial) using the given mass and radius of the merry-go-round.
2. Step 2: Calculate the final angular velocity (ωfinal) by rearranging the formula Iω = L and solving for ω.
3. Step 3: Convert the final angular velocity from rad/s to rpm by multiplying it by (1 min)/(2π rad).

After performing these calculations, the final angular velocity is found to be 27.27 rpm.