Answer:
ωM = 1.7 rad/s
vM = 3.4 m/s
ωA = 1.7 rad/s
vA = 1.7 m/s
Explanation:
Calculation of the angular speed (ω)
We use the following formula for circular motion:
ω = θ / t Formula (1)
Where:
ω: angular speed (rad/s)
θ:angle that the particle travels (rad)
t: time interval (s)
Equivalence
1 revolution = 2π rad
Data
θ= 1 revolution = 2π rad
t = 3.7 s
We replace data in the formula (1):
ω = (2π rad) / (3.7s )= 1.7 rad/s
Because the angular speed depends only on the number of turns in a time interval then Mary's angular speed (ωM) is equal to Alex's angular speed (ωA).
ωM = ωA = 1.7 rad/s
Calculation of the tangential speed (v)
We use the following formula for circular motion:
v = ω*r Formula (2)
Where:
v : tangential speed (m/s)
ω: angular speed ( rad/s)
r : radius of the circular path (m)
Data
ωM = ωM = ω= 1.7 rad/s
rM = 2m : Mary's circular path radius
rA = 1m : Alex's circular path radius
We apply the formula (2) to calculate v:
vM = ω* rM = (1.7) (2) = 3.4 m/s
vA = ω* rA = (1.7) (1) = 1.7 m/s
