Question

Two children, Ahmed and Jacques, ride on a merry-go-round. Ahmed is at a greater distance from the axis of rotation than Jacques. Which of the following are true statements? (There could be more than one correct choice.) Choose all that apply. Jacques and Ahmed have the same tangential speed.
A. Ahmed has a greater tangential speed than Jacques.
B. Jacques has a greater angular speed than Ahmed.
C. Jacques has a smaller angular speed than Ahmed.
D. Jacques and Ahmed have the same angular speed.

Answer 1

Answer:

A. Ahmed has a greater tangential speed than Jacques.

D. Jacques and Ahmed have the same angular speed.

Explanation:

Kinematics of the merry-go-round

The tangential speed of the merry-go-round is calculated using the following formula:

v = ω*R

Where:

v is the tangential speed in meters/second (m/s)

ω is the angular speed in radians/second (rad/s)

R is the angular speed in meters (m)

Data

dA = RA  : Ahmed distance to the axis of rotation

dJ = RJ   : Jacques distance to the axis of rotation

Problem development

We apply the formula (1)

v = ω*R

vA= ω*RA : Ahmed  tangential speed

vJ= ω*RJ  :  Jacques  tangential speed

Ahmed is at a greater distance from the axis of rotation than Jacques, then,

RA ˃ RJ and Ahmed and Jacques have the same  speed ω, then:

vA ˃ vJ