# Introduction To Physics (PHYS 111N) Rotational Motion

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which child moves with greater magnitude of linear velocity?-HW8: Rotational motion

University

Old Dominion University

Course

Introduction to Physics (PHYS 111N)

Linear and Rotational Quantities Conceptual Question

A merry-go-round is rotating at constant angular speed. Two children are riding the merry-go-round: Ana is riding at point A

and Bobby is riding at point B.

Part A

Which child moves with greater magnitude of linear velocity?

Hint 1. Distinguishing between linear velocity and angular velocity

Ana’s (or Bobby’s) linear velocity is determined by the actual distance traveled (typically in meters) in a given time

interval. The angular velocity is determined by the angle through which (s)he rotates (typically in radians) in a

given time interval.

Part B

Who moves with greater magnitude of angular velocity?

Hint 1. Distinguishing between velocity and angular velocity

Ana’s (or Bobby’s) velocity is determined by the actual distance she (he) travels (typically in meters) in a given

time interval. Her (His) angular velocity

Part C

Who moves with greater magnitude of tangential acceleration?

Hint 1. Distinguishing tangential, centripetal, and angular acceleration

Ana’s tangential and centripetal acceleration are components of her acceleration vector. During circular motion, if

Ana’s speed is changing (meaning the merry-go-round is speeding up or slowing down) she will have a nonzero

tangential acceleration. However, even if the merry-go-round is turning at constant angular speed, she will

experience a centripetal acceleration, because the direction of her velocity vector is changing (you can’t move

along a circular path unless your direction of travel is changing!).

Both tangential and centripetal accelerations have units of , since they are the two-dimensional

components of linear acceleration. Angular acceleration, on the other hand, is a measure of the change in Ana’s

angular velocity. If her rate of rotation is changing, she will have a nonzero angular acceleration. Thus, angular

acceleration has units of .

Part D

Who has the greater magnitude of centripetal acceleration?

Hint 1. Distinguishing tangential, centripetal, and angular acceleration

Ana’s tangential and centripetal acceleration are components of her acceleration vector. For circular motion, if

Ana’s speed is changing (meaning the merry-go-round is speeding up or slowing down) she will have a nonzero

tangential acceleration. However, even if the merry-go-round is turning at constant angular speed, she will

experience a centripetal acceleration, because the direction of her velocity vector is changing (you can’t move

along a circular path unless your direction of travel is changing!).

Both tangential and centripetal accelerations have units of , since they are the two-dimensional

components of linear acceleration. Angular acceleration, on the other hand, is a measure of the change in Ana’s

angular velocity. If her rate of rotation is changing, she will have a nonzero angular acceleration. Thus, angular

acceleration has units of .

Part E

Who moves with greater magnitude of angular acceleration?

Hint 1. Distinguishing tangential, centripetal, and angular acceleration

Ana’s tangential and centripetal acceleration are components of her acceleration vector. For circular motion, if

Ana’s speed is changing (meaning the merry-go-round is speeding up or slowing down) she will have a nonzero

tangential acceleration. However, even if the merry-go-round is turning at constant angular speed, she will

experience a centripetal acceleration, because the direction of her velocity vector is changing (you can’t move

along a circular path unless your direction of travel is changing!).

Both tangential and centripetal accelerations have units of , since they are the two-dimensional

components of linear acceleration. Angular acceleration, on the other hand, is a measure of the change in Ana’s

angular velocity. If her rate of rotation is changing, she will have a nonzero angular acceleration. Thus, angular

acceleration has units of .

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