Colossus is a Ferris wheel located at the 1904 World's Fair section of Six Flags St. Louis in Eureka, Missouri. It has a mass of 1.6 x 105 kg and has a diameter of 50.3 m and turns at 1.5 rev/min. Assuming all of the mass is on the circumference of the wheel, a) what is its moment of inertia? b) what is its kinetic energy? c) what is the tangential velocity on the circumference?

Ventilation fan in a house, the length of each blade is 0.25 m, rotating at a constant angle of 20 rpm, the tangential velocity of the outer end of one blade, and its tangential acceleration respectively is equal to: Choose and solve steps a- 0.2m/s , 2m/s2  b- 5.0m/s ,2m/s2  c- 0.52m/s , 0m/s2 d- 20m/s ,0m/s

A hollow sphere rolls without slipping down a ramp that is 3.5 m long. the ramp is inclined at an angle of 20˚ with the horizontal. Use the conservation of energy to find the speed of the sphere at the bottom of the slope if it starts from rest. ( I= 2/3 m R2 )

What is the kinetic energy of a 123 cm long thin uniform rod with a mass of 458 g that is rotating about its center at 4.0 rad/s? Give your answer in Joules.

Two astronauts, each having a mass M, are connected by a rope of length d having negligible mass. They are isolated in space, moving in circles around the point halfway between them at speed v. c) By pulling on the rope, the astronauts shorten the distance between them to d/2. What is the new angular momentum of the system?d) What are their new speeds?e) What is the new rotational energy of the system?f) How much work is done by the astronauts in shortening the rope?

A truck with 0.420 m radius tires travels at 42 m/s. part a) What is the angular velocity of the rotating tires in radians per second?  part b) What is the angular velocity of the rotating tires in rev/min?

28.  An elliptical orbit can be analyzed using conservation of angular momentum and mechanical energy.  The distance between Earth, mass 5.972 × 1024 kg, and Sun, mass 1.989 × 1030 kg, varies from 147 to 152 Gm.  (a) Use the formula UG = – Gm1m2/r to find the change in potential energy that occurs moving from the farthest distance to the nearest.  (b) Given that the speed of Earth at its farthest point is 29.29 km/s, use conservation of energy to find its speed at the nearest point.  (c) Calculate the angular momentum of Earth at each extreme and show that it is equal.29.  Use concepts from the previous problem to find the speed of Pluto at each extreme of its orbit about the Sun – distance varying from 4.44  × 1012 m to 7.38 × 1012 m.  Hint:  use a system of equations based on conservation of energy and angular momentum. P.S. I already solved 28 but I don't know how to do 29.

Arithmetic question. Write only the final value of the answer.   Suppose you did the rotational dynamics labs with a 200g solid sphere. The sphere was placed at rest at the 100cm mark on the track which is inclined at 150 angle with the table. What is the translational kinetic energy in (J) of the sphere as it leaves 0 mark of the track? Write your answer with TWO decimal places.

A turntable plays a vinyl with a mass of 0.186 kg and with a diameter of 0.089 meters. The vinyl rotates about an axis through its center with 0.698 J of kinetic energy. What is the speed (in m/s) of a point on the rim? The moment of inertia of the vinyl is I = (1/2)MR2