7. You are asked to design a turntable that is 55.8 cm in diameter that has a kinetic energy of 0.250 J when it is turning at 45.0 rev/min. a. What must its moment of inertia be? b. If you make the turntable in the shape of a uniform solid disk, what mass would it have?

3 1. A uniform solid sphere rolls without slipping down a 28° inclined plane. What is the acceleration of the sphere's center of mass? The moment of inertia of a uniform solid sphere about an axis that passes through its center = mr². The moment of inertia of a uniform solid sphere about an axis that is tangent to its surface = 7/5mr². m/s² E D C 4 22 R F % 5 V T G tv B MacBook Air 22 Y H 7 5 N 00 8 ZA 3 ( 9 K MOSISO O O V P command DUI 04 M option

A 6 cm diameter, 550 g solid sphere is released from rest at the top of a 2.0 m long, 35° incline. It rolls, without slipping, to the bottom. a. What is the sphere’s angular velocity at the bottom of the incline?b. What fraction of its kinetic energy is rotational?

Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.5 m diameter and a mass of 250 kg. A motor spins up the flywheel with a constant torque of 50N⋅m50N⋅m. How long does it take the flywheel to reach top angular speed of 1200 rpm?   Show a diagram

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A pulley is bolted to a wall as shown. The pulley is a flat disk of mass mp, radius R and moment of inertia I = mpR². A mass MH hangs from it by a rope that is wound about the pulley and does not slip. a. Give an appropriate force diagram for each of the two masses. b. Write ALL equations necessary to solve for the linear acceleration of MH. B мн

Baby Huey rolls a hollow sphere of mass M and radius R up a hillside, giving it an initial kinetic energy of Ki.  It rolls over the top of the hill of height h and keeps going.  The ball rolls without slipping the whole way, but it loses Wnc due to non-conservative forces between the foot of the hill and the top. a.  If M = 6.82 kg and R = 10.9 cm, find its rotational inertia. b.  Find the translational velocity at the top of the hill.

A 0.1 kg solid disc has a radius of 0.2 m. The moment of inertia of a solid disc is I = ½ m r2. EXAM  The disc initially rolls with a velocity of 2 m/s along a horizontal surface. It then rolls up a ramp and briefly stops when it reaches a height h.  The disc rolls without slipping on both surfaces.  a) What is the angular velocity of the disc when it is on the horizontal surface?  b) What is the speed of a point on the very top of the disc when the disc is on the horizontal surface?  c) Use Conservation of Energy to find the maximum height of the disc, h.  d) If the disc were replaced with a thin ring (same mass, same radius, same initial speed), would it roll higher, less high, or the same height? No calculations required. Briefly explain your answer!  e) If there were no friction (the disc slides instead of rolling), but the disc still has the same initial speed, would it roll higher, less high, or the same height?

A 50 g solid sphere is rolling without slipping along a horizontal surface at a speed of 800 cm/s. It comes to a point where the surface rises 30 ̊above the horizontal. Neglect energy losses due to friction. a. What is the total energy of the rolling sphere? b. To what vertical height will it roll up the plane?

A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 280 N applied to its edge causes the wheel to have an angular acceleration of 0.946 rad/s2.    What is the moment of inertia of the wheel? What is the mass of the wheel? If the wheel starts from rest, what is its angular velocity after 5.40 s have elapsed, assuming the force is acting during that time?