Question

# A compact disc rotates from rest up to an angular speed of 31.6 rad/s in a...

A compact disc rotates from rest up to an angular speed of 31.6 rad/s in a time of 0.913 s.

(a) What is the angular acceleration of the disc, assuming the angular acceleration is uniform?

(b) Through what angle does the disc turn while coming up to speed?

(c) If the radius of the disc is 4.45 cm, find the tangential speed of a microbe riding on the rim of the disc.

____________ m/s

(d) What is the magnitude of the tangential acceleration of the microbe at the given time?

_____________ m/s2

(Use the values from ABOVE)

(a) What are the angular speed and angular displacement of the disc 0.320 s after it begins to rotate?

(b) Find the tangential speed at the rim at this time.

_____________ m/s

here,

final angular speed , w = 31.6 rad/s

time taken , t = 0.913 s

a)

let the angular accelration be alpha

w = w0 + alpha * t

31.6 = 0 + alpha * 0.913

b)

the angle travelled , theta = w0 * t + 0.5 * alpha * t^2

theta = 0 + 0.5 * 34.6 * 0.913^2 rad

c)

radius , r = 4.5 cm = 0.045 m

the tangential speed , v = r * w

v = 0.045 * 31.6 = 1.42 m/s

d)

the magnitude of tangential accelration , a = r * alpha

a = 0.045 * 34.6 m/s^2

a = 1.56 m/s^2

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