A 10.0- kg cylinder rolls without slipping on a rough surface.At an instant when its center of gravity has a speed of 10.0 m/s,determine (a) the translational kinetic energy of its center ofgravity, (b) the rotational kinetic energy about its center ofgravity, and (c) its total kinetic energy.

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

A thin, hollow sphere of mass 2.30 kg and radius 0.610 m is rolling on a horizontal surface with a constant angular speed of 61.0 rpm. What fraction of the kinetic energy is translational kinetic energy, and what fraction of the kinetic energy is rotational kinetic energy?

A playground merry-go-round with an axis at the center (radius R = 1.5 m and rotational inertia | = 1.33 x 103 kgm²) is initially rotating at angular velocity wo = 1.1 rad/s (counter-clockwise). A girl of mass m = 39 kg is running at speed vo = 3.3 m/s in a direction tangent to the disk of the merry-go-round, intending to jump on to the point labeled with the green "x" (she is indicated by the purple circle in the figure). What is the angular momentum of the girl relative to the rotation axis of the merry-go-round? Your answer should be in kgm²/s, but enter only the numerical part in the box. R Wo

The spool has a mass of 30 kg and a radius of gyration of ko= 0.4 m, and r is 0.3 m. Neglect the mass of the cord. If the 10-kg block A is released from rest, determine the distance the block must fall in order for the spool to attain an angular velocity - 10 rad/s and the cord force during the motion. OF

Assume mars is a uniform solid sphere of mass 6.42x10^23 kg and a radius 3390 km.The length of a day on mars is 24 hours and 37 min. What is the rotational kinetic energy of the planet about its axis.

A baseball has a mass of 0.15 kg and radius 3.7 cm. In a baseball game, a pitcher throws the ball with a substantial spin so that it moves with an angular speed of 37 rad/s and a linear speed of 51 m/s Assuming the baseball to be a uniform solid sphere, determine the rotational and translational kinetic energies of the ball in joules. КЕ Frotational KEtranslational

A string is wrapped severaltimes around the rim of a small hoopwith radius 8.00 cm and mass 0.180 kg.The free end of the string is held inplace and the hoop is released from rest. After the hoop hasdescended75.0 cm, calculate (a) theangular speed of the rotating hoop and(b) the speed of its center.

A uniform solid disk of mass m = 2.99 kg and radius r = 0.200 m rotates about a fixed axis perpendicular to its face with angular frequency 6.05 rad/s. (a) Calculate the magnitude of the angular momentum of the disk when the axis of rotation passes through its center of mass. kg • m2/s (b) What is the magnitude of the angular momentum when the axis of rotation passes through a point midway between the center and the rim? kg • m2/s

A uniform solid disk of mass m = 2.99 kg and radius r = 0.200 m rotates about a fixed axis perpendicular to its face with angular frequency 5.99 rad/s. (a) Calculate the magnitude of the angular momentum of the disk when the axis of rotation passes through its center of mass. |kg · m2/s (b) What is the magnitude of the angular momentum when the axis of rotation passes through a point midway between the center and the rim? |kg · m2/s