A thin, very light wire is wrapped around a drum that is free to rotate. The free end of the wire is attached to a ball of mass m. The drum has the same mass m. Its radius Is R and its moment of inertia is I = (1/2)mR. As the ball falls, the drum spins. At an instant that the ball has translational kinetic energy K, what is the rotational kinetic energy of the drum? Drum m O a. none of these. Ob. K/2 Oc.2K O d. K Oe. K/4

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

A bicycle racer is going downhill at 13.5 m/s when, to his horror, one of his 2.17 kg wheels comes off when he is 52.0 m above the foot of the hill. We can model the wheel as a thin-walled cylinder 85.0 cm in diameter and neglect the small mass of the spokes. Part A How fast is the wheel moving when it reaches the foot of the hill if it rolled without slipping all the way down? ΕΠΙ ΑΣΦ VAΣ+ ? V = 33 Submit Previous Answers Request Answer × Incorrect; Try Again Part B m/s How much total kinetic energy does the wheel have when it reaches the bottom of the hill? Kf = ΜΕ ΑΣΦ 2406 ? J

A figure skater with rotational inertia Iskater is spinning with angular speed ω. She pulls her arms in, decreasing her rotational inertia to one-third its original value. Her new angular speed is ____ . Select one: a. 3–√3ω  b. ω3–√3  c. 3ω  d. ω/3  e. ω

A long, thin uniform rod of length 1.29m and mass 2.08kg is pivoted about a horizontal, frictionless pin passing through one end. The rod is released from one end in the vertical position. L y Pivot x At the instant the rod is horizontal, find its angular speed. Submit Answer Tries 0/10 At the instant the rod is horizontal, what is its angluar acceleration? Submit Answer Tries 0/10 At the instant the rod is horizontal, what is the magnitude of its x-component of acceleration at its centre of mass? Submit Answer Tries 0/10 At the instant the rod is horizontal, what is the magnitude of its Y-component of acceleration at its centre of mass? Submit Answer Tries 0/10

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 turntable plays a vinyl with a mass of 0.186 kg and with a diameter of 0.089 meters. The vinyl rotates about an axis through its center with 0.698 J of kinetic energy. What is the speed (in m/s) of a point on the rim? The moment of inertia of the vinyl is I = (1/2)MR2