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## You are sitting on a merry-go-round at a distance of 2m from its center. It spins 15 times in 3 min. What distance do you move as you make o

Question

You are sitting on a merry-go-round at a distance of 2m from its center. It spins 15 times in 3 min. What distance do you move as you make one revolution? What is your angular speed in RPM? What is your linear speed in meters per SECOND?

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Physics
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2021-09-02T09:38:35+00:00
2021-09-02T09:38:35+00:00 1 Answers
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## Answers ( )

Answer:A) 12.57 m

B) 5 RPM

C) 3.142 m/s

Explanation:A) Distance covered in 1 Revolution:The formula that gives the relationship between the arc length or distance covered during circular motion to the angle subtended or the revolutions, is given as follows:

s = rθwhere,

s = distance covered = ?

r = radius of circle = 2 m

θ = Angle = 2π radians (For 1 complete Revolution)

Therefore,

s = (2 m)(2π radians)s = 12.57 mB) Angular Speed:The formula for angular speed is given as:

ω = θ/twhere,

ω = angular speed = ?

θ = angular distance covered = 15 revolutions

t = time taken = 3 min

Therefore,

ω = 15 rev/3 minω = 5 RPMC) Linear Speed:The formula that gives the the linear speed of an object moving in a circular path is given as:

v = rωwhere,

v = linear speed = ?

r = radius = 2 m

ω = Angular Speed in rad/s = (15 rev/min)(2π rad/1 rev)(1 min/60 s) = 1.571 rad/s

Therefore,

v = (2 m)(1.571 rad/s)v = 3.142 m/s