Question

Please show work, I'm having trouble answering these :(

1)A bicycle with 0.3 m radius wheels, is moving such that the angular speed of each wheel is 75 rad/s. If the bicyclist then applies the brakes and the wheels slow with an angular acceleration of -15 rad/s2, how many revolutions will each wheel make before the bike stops?
A. 188 revolutions

B. 1.07e4 revolutions

1C.14.7 revolutions

D. 62.7 revolutions

E.29.8 revolutions

2)You tie the loose end of a 0.1 kg yo-yo string to your finger and then release the yo-yo so that it spins down toward the ground (the yo-yo is released from rest and the end of the string tied to your finger remains motionless). After the yo-yo falls a distance of 0.9 m, it has a translational speed of 4 m/s and an angular speed of 180 rad/s. What is the moment of inertia of the yo-yo? You may neglect air resistance.
A. 9.9e-7 kg m2

B. 4.5e-5 kg m2

C. 4.4e-6 kg m2

D. 5.1e-6 kg m2

E. 6.0e-6 kg m2

3)  Water falls onto a water wheel causing it to rotate. Consider an instant when the water wheel is initially motionless and then 100 kg of water hits tangent to the wheel at a radius of 2 m (this water can be treated like a point mass). If the moment of inertia of the water wheel is 3000 kg?m2,what is the angular speed of the water wheel immediately after the water has hit it?
A. 0.53 rad/s

B. 0.42 rad/s

C. 0.34 rad/s

D. 0.29 rad/s

E. 0.92 rad/s

4)  A mass is connected to a spring with constant k = 200 N/m, and oscillates back and forth such that the acceleration, as a function of time, is given by ?? = 70 ?????? (17??) m/s2. What is the total mechanical energy of this spring/mass system?

Answer 1