A merry-go-round in a park has a radius of 6 m and an angular velocity of 0.2 re

Question

A merry-go-round in a park has a radius of 6 m and an angular velocity of 0.2 rev/sec. A 90 kg person sits on the outer edge of the disk as it rotates.

A) Calculate the rotational velocity of the merry go round in radians/sec.
B) If the teacher releases a stone, what will be the stone's horizontal velocity?
C) If the stone is released from a height of 3.2 m, what horizontal distance is covered by the stone before it hits the ground?
D) How much time does it take for the person to go around one time?
E) What is the angular velocity of the person standing at 3m?
F) What is the person's linear velocity?

Explanation / Answer

a) Rotational velocity = 0.2 rev/s = 0.2 x 2 rad/s = 0.4 or 1.26 rad/s

b) v= r = 1.26 xx 6 = 7.54 m/s

c) h = gt2 /2

t = (2 x 3.2 / 9.81) = 0.808 s

so distance = vt = 7.54 x 0.808 = 6.09 m

d) angular velocity is 0.2 rev in one second so for one revolution t = 1/0.2 = 5 sec

e) angular velocity is = 0.2 rev/s   or 1.26 rad/s

f) linear velocity = r = 1.26 x 3 = 3.78 m/s

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