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Fundamentals Of Physics
Found in: Page 294

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Short Answer

A vinyl record on a turntable rotates at 3313 rev/min. (a) What is its angular speed in radians per second? What is the linear speed of a point on the record (b) 15  cm and (c) 7.4  cm from the turntable axis?

a) Angular speed is 3.5  rad/sec.

b) Linear speed at 15  cm is 52  cm/s.

c) Linear speed at 7.4 cm is 26 m/s.

See the step by step solution

Step by Step Solution

Step 1: Given

ω=3313 rev/min

Step 2: Determining the concept

For smaller angular displacements, the linear velocity can be described as the product of the angular velocity and the radius of the circular path in which the Here particle is traveling.Use the formula for linear velocity in terms of radius and angular speed. Linear velocity is written as the product of radius and angular velocity.


where, v is velocity, r is radius and ω is angular velocity.

Step 3: (a) Determining the angular speed

Here, first convert 3313rev/min into rad/sec as follows:

ω=1003 rev/min×0.1047  rad/sec1 rev/min

ω= 3.5 rad/s

Hence,angular speed is 3.5  rad/s.

Step 4: (b) Determining the linear speed at 15  cm

Now, use the following formula to find linear speed:


v=0.15 m×3.5 rad/s

v= 0.52 m

Hence,linear speed at 15  cm is 52  cm/s .

Step 5: (c) Determining the linear speed at 7.4  cm

Now, use the following formula to find linear speed:


v=0.074 m×3.5 rad/s

.v=0.26 m/s

Hence, linear speed at 7.4 cm is .26 m/s

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