Question

A child exerts a tangential 56.8 n force on the rim of a disk-shaped merry-go-round with a radius of 2.29 m . if the merry-go-round starts at rest and acquires an angular speed of 0.9250 rev/s in 3.00 s , what is its mass?

Answer 1

Calculating the merry-go-round's mass involves using physics equations for rotational motion, including torque and moment of inertia, and applying them to the provided force, angular velocity, and time data.

Step-by-step explanation:

The question concerns calculating the mass of a merry-go-round based on the force applied, angular acceleration, and time taken to reach a certain angular velocity. To solve this, we would apply Newton's second law for rotation and the equation for angular acceleration to find the moment of inertia, and subsequently the mass of the merry-go-round since the moment of inertia for a disk is ½MR².

The key steps involve:

1. Calculating the angular acceleration (α) using the change in angular velocity (ω) and time (t).
2. Using the torque (τ) generated by the applied force and the radius (r), calculate the moment of inertia (I).
3. Since I = ½MR² for a disk, solve for the mass M.

This process requires understanding of the physical concepts of rotational motion, which involve aspects such as torque, moment of inertia, angular velocity, and angular acceleration.