Answer:
(a) ωM=ωA
(b) vA = (0.625)vM
Explanation:
The tangential velocity of the body is calculated by the following formula:
v = ω*R Formula (1)
where:
v is the tangential speed of the body in feet over second (ft/s)
ω is the angular speed in radians over second (rad/s)
R is the radius of the the body in the circular path in meters (m)
(a) What is Mary's angular speed ωM compared to that of Alex's angular speed ωA
The angular speed of Mary and Alex is determined by the angular speed of the carousel ( ωC),therefore it is the same for both:
ωM=ωC , ωA=ωC
ωM=ωA
(b) What is Mary's tangential speed vM compared to that of Alex's tangential speed vA?
Data:
RM = 8 ft : Mary radio
RA = 5 ft : Alex radio
We apply the formula (1)
v = ω*R
vM = ωC *8 : Mary's tangential speed
vA = ωC *5 : Alex's tangential speed
We establish the relationship between vA and vM like this:
vA/vM = (ωC*5) / (ωC*8)
We cancel ωC
vA = (5/8)vM
vA = (0.625)vM