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)

distance = 523 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