A compact disc (CD) in a player spins about its central axis
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics
Problem
A compact disc (CD) in a player spins about its central axis. When the player first begins reading data from the outer edge, the disc rotates at 480rev min−1 (revolutions per minute). The outer data track is located 5.5cm from the axis, and the innermost data track that can be read at this rotation rate is 2.0cm from the axis.
(1) Part 1: Convert the disc’s rotation rate to angular speed in SI units.
(2) Part 2: Determine the linear speed of a point on (i) the outer data track and (ii) the innermost data track at this rotation rate.
(3) Part 3: As the disc slows down later in the track, its angular speed decreases uniformly with an angular deceleration of 30rads−2. Calculate the tangential (linear) acceleration experienced simultaneously by points on the outer and inner data tracks.
(4) Part 4: Without performing further calculations, explain why the ratio of the linear speeds you found in part (b) equals the ratio of the radial positions of the two tracks.