1) A record is spinning at the rate of 25 rpm. If a ladybug is sitting 10 cm from the
center of the record:
a) What is the rotational speed of the ladybug? (in rev/sec)
B)What is the frequency of the ladybug's revolutions? (in Hz)
C)What is the tangential speed of the ladybug? (in cm/sec)
d)
After 20 seconds, how far has the ladybug traveled? (in cm)

Explanation:

( a ) The rotational speed of the ladybug = 25 r.p.m = 25/60 r.p.s

= 5/12 rev/sec

( b ) The definition of frequency is the number of rotations per second .

Here the number of rotations per second is 5/12 . Thus frequency = 5/12 Hz

( c ) The tangential speed is v = angular velocity x radius of rotation

The angular velocity ω = 2π x n , where n is the number of rotations per second

Thus angular velocity = 2π x 5/12   = 5π/6 rad/sec

The linear velocity = angular velocity x distance from center of record

Thus tangential speed = 5π/6 x 10 = 25π/3 cm/sec

Angular displacement in 20 sec = ω x t = 5π/6 x 20 = 50π/3 rad

Linear displacement = angular displacement x distance from center of record

= 50π/3 x 10 = 500π/3 = 523 cm

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