A vinyl record (disk) starts from rest and then rotates about its central axis r

Question

A vinyl record (disk) starts from rest and then rotates about its central axis reaching playing speed of 33 1/3 rmp in 2.5 seconds. The record has a diameter of 32 cm and a mass of 0.40kg. in the interval from t=0 to t=2.5 seconds calculate

a. the final angular velocity in radians/sec

b. the average linear speed of a point on the outside edge of the disk

c. the total angular displaement

d. the amount of torque required

e. calculate the final angular velocity of the two records when another record, (disk with a diameter of 24cm and a mass of 0.20kg) drops down on top of the original

Explanation / Answer

w = 33 1/3 rpm = (33 + 1/3) x 2pi / 60 = 3.49 rad/s

b) average w = 3.49/2 = 1.75 rad/s

v = w.r = 1.75 x 0.16 = 0.279 m/s

c) angular displacement = wi x t + alpha x t^2 /2

alpha = 3.49 / 2.5 = 1.40 rad/s2

ang. dis. = 0 + 1.40 x 2.5^2 /2 = 4.36 rad

d) torque = I x alpha = (0.40 x 0.16^2 /2) x 1.40 = 7.168 x 10-3 N.m

e) angular momentum (Iw) conserrvation ,

(0.40 x 0.16^2 /2) x 3.49 = [(0.40 x 0.16^2 /2) + (0.20 x 0.12^2 /2)] w

w = 2.72 rad/s

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