03.2 You are sitting on the edge of a merry-go-round of radius 1.80 m. When you
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Question
03.2 You are sitting on the edge of a merry-go-round of radius 1.80 m. When you are at the northern-most point of your motion, you have clockwise angular velocity of 30.0 rpm and you start to drag your foot on the ground. By the time you have made half a revolution, you are moving with angular velocity 15.0 rpm. Assume constant angular acceleration. a) What is the magnitude and direction of your linear acceleration when it is at the southern-most point of its trajectory, after making half of a revolution? b) If you continue to drag your foot, when and where does the merry-go-round stop?Explanation / Answer
initial velocity = 30 rpm or 3.1416 rad/sec
final velocity = 15 rpm or 1.57 rad/sec
distance travelled in half revolution = pi rad
by third equation of motion
v^2 = u^2 + 2as
1.57^2 = 3.1416^2 + 2 * a * pi
a = -1.1785 rad/sec^2
linear acceleration = angular acceleration * radius
linear acceleration = -1.1785 * 1.8
magnitude of linear acceleration = 2.1213 m/s^2
direction is toward east
if merry go round stops its final velocity will be 0 so,
0 = 3.1416^2 + 2 * (-1.1785) * s
s = 4.187 rads or 0.66 rev
after 0.66 revolution of 4.187 rads it will stop
by first equation of motion
v = u + at
0 = 3.1416 - 1.1785 * t
t = 2.665 sec
it will stop after 2.665 sec
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