Question

A compact disc rotates at 500 rev/min. If the diameter of the disc is 120 mm, (a) What is the tangential speed of a point at the edge of the disc? (b) At a point halfway to the center of the disc?

Answer 1

Answer:

(a) the tangential speed of a point at the edge is 3.14 m/s

(b) At a point halfway to the center of the disc, tangential speed is 1.571 m/s

Explanation:

Given;

angular speed of the disc, ω = 500 rev/min

diameter of the disc, 120 mm

radius of the disc, r = 60 mm = 0.06 m

(a) the tangential speed of a point at the edge is calculated as follows;

$\omega = 500 \ \frac{rev}{\min} \times \frac{2\pi \ rad}{1 \ rev} \times \frac{1 \min}{60 \ s} = 52.37 \ rad/s$

Tangential speed, v = ωr

                               v = 52.37 rad/s  x 0.06 m

                              v = 3.14 m/s

(b) at the edge of the disc, the distance of the point = radius of the disc

   at half-way to the center, the distance of the point = half the radius.

r₁ = ¹/₂r = 0.5 x 0.06 m = 0.03 m

The tangential velocity, v = ωr₁

                                       v = 52.37 rad/s x 0.03 m

                                       v = 1.571 m/s