1.Obama is sitting on a high-tech, frictionless office chair. The combined mass

Question

1.Obama is sitting on a high-tech, frictionless office chair. The combined mass of Obama and the chair is 70 kg. Obama holds a 5-kg shake-weight (a weight used to work out), 1 m away from himself with his arms straight out. A disgruntled Joe Biden applies a torque to Obama of 17 N×m for 5 s. To Biden’s dismay, Obama enjoys spinning and decides to go faster, so he brings the shake-weight in closer to his body. If Obama reaches 9 rad/s, how close does the shake-weight need to be to his body? Treat Obama and the chair as a “cylindrical” shape with a radius of 0.5 m.

2. Skateboarder Kevin, with a mass of 62 kg, is skateboarding on the Moon. He launches off a 45-degree ramp with an initial speed of 5 miles per hour. Kevin then lands on top of a small hill that is at the same height as the top of the ramp. If the Moon’s mass is 7.35 x 1020 kg, and the Moon’s radius is 1,737 km, how far did Kevin travel?

I am sorry that there is no picture for these questions.

Since I need to know how to solve them, please show me all of steps.

Explanation / Answer

1.
Initial I of obama = Io + 5*1^2 = Io + 5
Final I of Obama = Io + 5r^2
now, [Io + 5][a] = 17
a = 17/[Io + 5]
w = 17*5/[Io+5] = 85/[Io+5]
conservation of angular momentum
[Io+5]*85/[Io+5] = [Io+5r^2]9
9.444 = Io + 5r^2 -- (1)
now Io = 70*0.5^2/2 = 8.75
so r = 37.2 cm

2.

R = v^2sin(2theta)/g = 5^2*6/9.8 = 15.30 miles [ g = 9.8/6 -> 1/6th of the earth's g]

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