A solid flywheel initially at rest undergoes a three-segment motion while mounted on…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A solid flywheel initially at rest undergoes a three-segment motion while mounted on a low-friction horizontal axle. Counter-clockwise rotation is defined as positive.
Segment 1: From t=0 to t=2.0s, the flywheel experiences a constant angular acceleration of +4.0rads−2.
Segment 2: From t=2.0s to t=3.0s, no external torques act on the flywheel.
Segment 3: Beginning at t=3.0s, a braking pad applies a constant torque that produces an angular acceleration of −3.0rads−2 until the flywheel comes momentarily to rest.
(a) Determine the angular velocity of the flywheel at the end of each of the three segments. Present each value with its correct sign.
(b) For Segment 3, calculate the time required for the braking pad to bring the flywheel momentarily to rest.
(c) Compute the angular displacement during each segment and state whether each displacement corresponds to counter-clockwise or clockwise physical rotation.
(d) Using your results from part (c), find the flywheel’s total angular displacement from t=0 until it momentarily stops at the end of Segment 3. Explain how the algebraic sign of the total displacement relates to the sequence of clockwise and counter-clockwise rotations that occurred.
(e) Sketch—on your own paper—a qualitatively accurate graph of angular velocity versus time for the entire motion, clearly labeling key numerical values determined in parts (a) and (b). Briefly describe two distinct time intervals on your graph where angular velocity and angular acceleration have the same sign and two intervals where they have opposite signs.