A water wheel is located in a river with a current running at 4.00 m/s. If the w

Question

A water wheel is located in a river with a current running at 4.00 m/s. If the wheel has a radius of 3.15 m, what is the angular speed of the waterwheel in rev/s? What is the radius of a geocentric orbit around the Earth? (A geocentric orbit is one that orbits the Earth once per day) Two masses, of mass 2.85 kg and 7.22 kg, are connected to the ends of a massless rod of length 1.61 m. (a) Find the moment of inertia for rotations around the center of the rod. (b) What is the angular momentum of the object when it rotates around the center of the rod with angular velocity 4.19 rev/s? What is the rotational kinetic energy of the Earth spinning around its axis? You can assume that the Earth is a uniform ball. If I push straight forward on the center of a 1.2 m-wide door with a force of 10.3 N, what torque do I exert on the door? The International Space Station (ISS) orbits the Earth once every 92.0 min (I know, it's fast). Assuming that the ISS has a circular orbit: (a) Find the radius of the ISS's orbit. How high above the surface of the Earth is the ISS (in miles)? (b) Find the tangential velocity of the ISS. (c) What is the centripetal acceleration of the ISS as it orbits Earth?

Explanation / Answer

1) relation between v and w is

v = rw

w = v/r = 4/3.15 = 1.269 rad/s = 0.202 rev/s

2) r = 42164 km

3) I = I1+I2 = (m1+m2)r^2 = (2.85+7.22)*0.805^2 = 6.52 kg m^2

L = I*w = 6.52*4.19*2*3.14 = 171.56 kg m^2/s

4) k = 1/2Iw^2 = 1/2*2/5*mr^2*w^2

w = 2pi/T

k = 1/5*mr^2*4pi^2/T^2

5) TORQUE = r*f = 12.36 Nm

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