A hollow sphere of mass M and radius R = 0.15 m, with rotational inertia I = kg · m2 about a line through its center of mass, rolls without slipping up a surface inclined at 0 = 30° to the horizontal. At a certain position, say at a height hi from the ground, the sphere's total kinetic energy (its center of mass kinetic energy plus its rotational kinetic energy) is 20 J. (Hint: The moment of inertia of such a halo sphere is I = translational speed of a point on the surface of the sphere is the same as the speed of the center of mass of the sphere) 0.040 MR. The (a) What ratio of this total kinetic energy is rotational? (b) What is the speed of the center of mass of the sphere at this position? When the sphere has moved d = 1 m up the incline from this (initial) position, using conservation of energy, find (c) its total kinetic energy and (d) the speed of its center of mass d = 1m R

You are riding your bicycle down the street at a speed of 16 m/s. Your bicycle's frame has a mass of 6.0 kg, and each of its two wheels has mass 2.2 kg and radius 0.34 m. Each wheel can be thought of as a hollow hoop (assuming that the rim has much larger mass than the spokes). What is the total kinetic energy of the bicycle (in Joules)?(take into account both the translational and rotational motion.)

A car is designed to get its energy from a rotating flywheel in the shape of a uniform, solid disk of radius 0.650 m and mass 600 kg. Before a trip, the flywheel is attached to an electric motor, which brings the flywheel's rotational speed up to 5.30 ✕ 103 rev/min. (a) Find the kinetic energy stored in the flywheel (in J).   (b) If the flywheel is to supply energy to the car as a 12.0 hp motor would, find the length of time in hours the car could run before the flywheel would have to be brought back up to speed.

A hollow sphere of mass M and radius R = 0.15 m, with rotational inertia I = 0.040 kg · m² about a line through its center of mass, rolls without slipping up a surface inclined at 0 = 30° to the horizontal. At a certain position, say at a height hi from the ground, the sphere's total kinetic energy (its center of mass kinetic energy plus its rotational kinetic energy) is 20 J. (Hint: The moment of inertia of such a halo sphere is I = MR². The translational speed of a point on the surface of the sphere is the same as the speed of the center of mass of the sphere) (a) What ratio of this total kinetic energy is rotational? (b) What is the speed of the center of mass of the sphere at this position? (5 points) 1 m up the incline from this (initial) position, using When the sphere has moved d conservation of energy, find (c) its total kinetic energy ), and (d) the speed of its center of mass