Please use 9.8 for gravity for any of the problems below. Show all work and round to the .000000 decimal place

fairground ride spins its occupants inside a flying saucer-shaped container. If the horizontal circular path the riders follow has an 8m radius, at how many revolutions per minute will the riders be subjected to a centripetal acceleration whose magnitude is 1.5 times that due to gravity?

A gyroscope slows from an initial rate of 39.63rad/s at a rate of 0.760rad/s². How long does it take to come to rest?

A large centrifuge is used to expose aspiring astronauts to accelerations similar to those experienced in rocket launches and atmospheric re-entries. At what angular velocity is the centripetal acceleration 8g if the rider is 12.92m from the center of rotation?

A playground merry-go-round has a mass of 145kg and radius of 1.513m and it is rotating with an angular velocity of 0.5rev/s. What is the centripetal force of a 22kg child on the edge of the merry-go-round?

A record has a scratch 14.10cm from the center that makes the record skip 47 times each minute. What is the linear speed of the scratch as it turns?

A soccer player extends her lower leg in a kicking motion by exerting a force with the muscle above the knee in the front of her leg. She produces an angular acceleration of 25rad/s² and her lower leg has a moment of inertia of 0.66kgm². What is the force exerted by the muscle if its effective perpendicular lever arm is 1.9cm?

A truck with 0.44m radius tires travels at 34.540m/s. What is the angular velocity of the rotating tires in rad/s?

A wheel rotates with a constant angular acceleration of 3.5rad/s². If the angular speed of the wheel is 2.690rad/s at t = 0, what is the angular speed of the wheel at 2.340s?