PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics
Problem
In a pottery studio, a heavy turntable of radius 0.15m can rotate freely about a fixed vertical axis. The turntable undergoes three successive phases of motion:
• Phase I (0≤t≤2.0s): Starting from rest, a constant net torque acts on the turntable, giving it a steady angular acceleration. At t=2.0s its angular speed is 16rads−1.
• Phase II (2.0s<t≤7.0s): The net torque is removed and the turntable spins at the constant angular speed reached at the end of Phase I.
• Phase III (t>7.0s): A brake applies a constant counter-torque, producing an angular deceleration of magnitude 4.0rads−2 until the turntable stops.
Answer the following questions in sequence, providing full calculations and reasoning.
(a) Calculate the angular acceleration during Phase I.
(b) Determine the duration of Phase III, i.e., the time required for the turntable to come to rest after the brake is applied at t=7.0s.
(c) Compute the total angular displacement of the turntable from t=0 until it stops.
(d) A small blob of clay placed on the rim remains stuck to the turntable throughout the entire motion. Find the total linear distance traveled by the blob from t=0 until the turntable stops.