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Chapter 5: Problem 6

Why is it easier for a child to stand nearer the inside of a rotating merry- go-round?

Short Answer

Expert verified
It's easier for a child to stand on the inside of a rotating merry-go-round because the centripetal force, which pulls them towards the outside, is smaller near the center of the merry-go-round due to a smaller radius from the rotation point.

Step by step solution

01

Understand Centripetal Force

Centripetal force is a force that makes a body follow a curved path. Its direction is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path. In the case of a merry-go-round, the centripetal force is directed towards the center of the merry-go-round.
02

Understand Angular Velocity

Angular velocity refers to how fast an object moves around a certain point. In the case of the merry-go-round, all riders, no matter where they stand, have the same angular velocity, for they complete a circle in the same period of time.
03

Apply Concepts to the Merry-Go-Round

When a merry-go-round spins, every point on it has the same angular velocity. However, those standing further from the center, the radius from the rotation point to the child is larger, and according to the formula for Centripetal force, i.e., \( F = m*r* \omega^2 \) (\(r\) is the radius, \( \omega \) is the angular velocity, \( m \) is the mass), the force required to keep them moving in a circular path is greater. So, for a child, it's easier to stand near the center, where this force (which they feel as a pulling sensation) is smallest.

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