Studying for my physics exam. Please help with review. An astronaut is working o
ID: 1446315 • Letter: S
Question
Studying for my physics exam. Please help with review. An astronaut is working on a circular space station. The space station is initially at rest. The astronaut then begins his daily exercise in which he runs laps around the station with a linear speed of 3.0m/s at the edge of the space station. Find the resulting angular velocity of the station. The mass of the astronaut is 80kg, the mass of the station is 1.0 × 105kg, and assume that the station has the shape of a disk of radius 30 m.
2. Consider a yo-yo that starts from rest and then moves downwards in a manner you have probably practiced a few times. Find the velocity of the yo-yo after it has moved a distance of 50 cm below the starting location. You may assume the yo-yo is a solid disk with the string wound around the outer edge.
Explanation / Answer
1.
suppose finally station rotate with angular speed, w.
then speed of astronaut will be v1 = v - wr .
Using angular momentum conservation,
initial angular momentum =final angular momentum
0 = ( m v1 r) - ( I w)
m (v - wr) r = ( M r^2 / 2)w
80 x (3 - 30w) x 30 = (10^5 x 30^2 / 2) w
3 - 30w = 18750 w
w = 1.597 x 10^-4 rad/s
2. on yo-yo:
mg - T = ma
Using, torque = I x alpha
r T = ( m r^2 / 2)(a/r)
T = ma/2
adding both equations,
mg - ma/2 = ma
a = 2g/3 = 6.53 m/s^2
Using v^2 - u^2 = 2ad
v^2 - 0 = 2(6.53)(0.50)
v = 2.56 m/s