A circular platform can rotate about a vertical axis through its center
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics
Problem
A circular platform can rotate about a vertical axis through its center. Consider the positive direction to be counter-clockwise (CCW).
At time t=0 the platform is rotating clockwise at 4.0rads−1. From t=0 to t=3.0s the platform experiences a constant angular acceleration of +1.5rads−2. After t=3.0s the net torque on the platform becomes zero so that its angular velocity then remains constant.
Answer the following, using clear reasoning that refers to signs, directions, and relationships among θ, ω, and α. Numerical work is expected only where explicitly requested.
(a) State the signs (positive or negative) of the initial angular velocity and of the angular acceleration. For each, indicate the corresponding direction of rotation.
(b) Without calculating exact values, sketch qualitatively the shape of a graph of angular velocity versus time from t=0 to t=5s. Clearly label the value of ω at t=0 and at t=3.0s and explain how you determined the qualitative features of the graph.
(c) Will the platform come to rest at any instant during the time interval 0≤t≤3.0s? Justify your answer with conceptual or algebraic reasoning, but do not solve for the exact time.
(d) During the interval 0≤t≤3.0s, does the platform undergo a net angular displacement in the clockwise or counter-clockwise direction? Explain how you reached your conclusion, citing the interplay between the signs of ω and α.