A 2.0-kg hoop rolls without slipping on a horizontal surface so that its center proceeds to the right with a constant linear speed of 6.0 m/s. What is the total kinetic energy of the hoop?

A thin, uniform rod has one of its end mounted at 3. point P and is free to rotate about an axle that passes through P in a direction perpendicular to the figure. The rod is of length 1.0 m and mass 0.3 kg. It is released from rest at the horizontal position shown in the figure. A small ball of mass 0.1 kg is placed on a frictionless floor 1.0 m below point P such that when the rod reaches the vertical position, it just hits the ball. Assume that once the rod hits the ball, they stick together and swing up until they come to a momentary stop at an angle 0. (a) perpendicular to the figure? You can check the table on slide 27 of the lecture notes if needed. (b) problem from the perspective of energy conservation] (c) analyze the problem from the perspective of conservation of angular momentum] What is the rotational inertia of the rod about the axle passing through P and What is the angular speed of the rod just before it hits the ball? [Hint: analyze the What is the angular speed of the…

A flywheel is a solid disk that rotates about an axis that is perpendicular to the disk at its center. Rotating flywheels provide a means for storing energy in the form of rotational kinetic energy and are being considered as a possible alternative to batteries in electric cars. The gasoline burned in a 492-mile trip in a typical midsize car produces about 3.30 x 10° J of energy. How fast would a 26.8-kg flywheel with a radius of 0.315 m have to rotate to store this much energy? Give your answer in rev/min. Number 6640184.43 Units rev/min

The ramp on the figure is 0.75 m high. The object is a 2.0 kg cylinder with radius of r = 0.10 m. The cylinder rolls from the top and reaches the bottom. A) What is its total kinetic energy at the bottom? B) What is its rotational kinetic energy, C) what is its translational kinetic energy?