A Compact Disc (CD) has a diameter of 12.0 cm, rotates at aconstant 207 rpm, and

Question

A Compact Disc (CD) has a diameter of 12.0 cm, rotates at aconstant 207 rpm, and has a total playing time of
74.0 minutes.

Please Show Solution Please!

a.) What is the angular velocity of the CD?
b.) What is the linear speed of a point on the edge of thedisc?
c.) What is the angular displacement of the CD during its totalplay time?
d.) What is the distance traveled by a point on the edge of theCD?
e.) What is the distance traveled by a point 4.00 cm from thecenter of the CD?
f.) What is the angular acceleration of the CD during its totalplay time?
g.) What is the tangential acceleration of a point on the edge ofthe CD?
h.) What is the centripetal acceleration of a point on the edge ofthe CD?

Explanation / Answer

a) Quite clearly angular velocity or is nothing butthe angle / unit time or in other words 207 rotaions can beconverted to equivalent angle in radians = 207 * 2 radiansalso time = 1minute = 60 sec thus angular velocity = 207*2/60 radian /sec = 21.68 rad/sec b) linear speed of a point on the edge is nothing but .Rm/sec = 21.68 * .06 = 1.3 m/sec c) angular displacement = angular velocity * total time =21.68 *74 *60 radians = 96259 radians d) distance traveled by any point on disk = total angulardistance * distance of the point from the centre = .06 * 96259 = 5775.55 m e) as above = .04*96259 = 3850 m f) since the rpm or the angular velocity is constant angular acceleration is 0 g) Since the tangential velocity of any point is constant i.e.= r where r is the distance from the center thus tangentialacceleration is 0 h) centripetal acceleration is 2r = 28.1m/sec2

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