IP Playing a CD The record in an old-fashioned record player always rotates at t

Question

IP Playing a CD The record in an old-fashioned record player always rotates at the same angular speed. With CDs, the situation is different. For a CD to play properly, the point on the CD where the laser beam shines must have a linear speed vt = 1.34 m/s , as indicated in the figure.(Figure 1)

Part A As the CD plays from the center outward, does its angular speed increase, decrease, or stay the same?

Part B Explain?

Part C Find the angular speed of a CD when the laser beam is 2.50 cm from its center. W=______rad/s

Part D Repeat part B for the laser beam 6.00 cm from the center.

Part E If the CD plays for 66.5 min, and the laser beam moves from 2.50 cm to 6.00 cm during this time, what is the CD's average angular acceleration?

Explanation / Answer

Given

Linear velocity vt = 1.34 m/s

Solution

A)

Decreases

B)

The angular velocity

= vt / r

Since vt is constant

1/r

the angular velocity is inversely proportional to the radius.

When the laser head move outward its radius increases, so the angular velocity decreases.

C)

r = 2.50 cm = 2.50 x 10-2 m

= vt/r

= 1.34/2.50 x 10-2

= 53.6 rad/s

D)

r = 6 cm = 6 x 10-2 m

’ = vt/r

’ = 1.34/6 x 10-2

’ = 22.33 rad/s

E)

t = 66.5 min

t = 66.5 x 60 s

t = 3990 s

= ’ -

= 22.33 – 53.6

= -31.27

Angular acceleration = /t

= -31.27 / 3990

= -0.0078371 rad/s2

= -7.84 x 10-3 rad/s2

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