A 2.30 kg solid, uniform disk of radius 0.140 m is released from rest at point A in the figure below, its center of gravity a distance of 1.70 m above the ground. The disk rolls without slipping to the bottom of an incline and back up to point B where it is launched vertically into the air. The disk then rises to its maximum height max HINT 1.70 m (a) At point B. find the disk's translational speed v. (in m/s). x m/s (b) At point B. find the disk's rotational speed (in rad/s). rad/s (c) At point C. find the disk's rotational speed we (in rad/s). rad/s (d) At point C. find the maximum height max of the disk's center of gravity (in m). at point C.

A hollow sphere with a radius R and a mass M (note that I = (2/3)MR^2 for a hollow sphere) rolls down an incline with an angle θ. Its acceleration down the ramp is given by: A. 5/3gsinθ B. gsinθ  C. 3/5gsinθ D. 1/2gsinθ A solid uniform disk with a radius R and a mass M (note that I = (1/2)MR^2 for a solid disk) rolls down an incline with an angle θ. Its acceleration down the ramp is given by: ⃝ A. 5/3gsinθ ⃝ B. gsinθ  ⃝ C. 2/3gsinθ  ⃝ D. 1/2gsinθ

A flat uniform circular disk (radius = 6.22 m, mass=320 kg) is initially stationary. The disk is free to rotate in the horizontal plane about a frictionless axis perpendicular to the center of the disk. A 51.0-kg person, standing 2.32 m from the axis, begins to run on the disk in a circular path and has a tangential speed of 3.00 m/s relative to the ground. Find the resulting angular speed (in rad/s) of the disk.

Two Thin rectangular sheets (0.28m x 0.47 m) are identical. In the first sheet the axis of rotation lies along the 0.28 inside, and in the second it lies along 0.47m side. The same torque is applied to each sheet. The first sheet starting from rest reaches its final angular velocity in 5.2 s. How long does it take for the second seat starting from rest to reach the same Angularer velocity?

A solid metal disk with moment of inertia I, radius R, and mass m1 can rotate freely about a frictionless axis passing through its center. A light string is wrapped around the disk and connects to a hanging mass m2. The hanging mass is released from rest at a distance d above the ground and accelerates downward with acceleration awhile the disk rotates through an angle q. a) Find an expression for the angular accelerationaof the diskin terms of m2, I, R, and any necessary constants. b) Find an expression for the time it takes for the hanging mass to reach the ground. Write your answer in terms of q, a, and any necessary constants. c) Find an expression for the angular velocity of the disk just before the hanging mass hits the ground. Write your answer in terms of q, a, and any necessary constants.

Wile E. Coyote wants to flatten the Road Runner. Wile E. puts food at a pre-determined distance from the edge of a cliff. While the Road Runner eats the food, Wile E. pushes a log down the hill. It rolls without slipping. The radius of the log is 0.3 m. The mass of the log is 80 kg. The rotational inertia of the log is given by I = ½ MR2 . The translational speed of the log just before it leaves the cliff horizontally is 16 m/s. The Road Runner is 10 m below the cliff. If the log is to successfully hit the Road Runner, the food must be place at a precise location from the base of the cliff which you will determine. a. Use only energy considerations and the fact that the log does not slip as it rolls to determine the height it started from, h, before it went over the cliff. b. Determine how far from the edge of the cliff the food needs to be placed so the log lands on the Road Runner. The rotating motion of the log in the air does not affect the motion of the log once it is in the air.…

A ball of mass M = 1.30 kg and radius r = 4.50 cm is attached to one end of a thin, cylindrical rod of length L = 14.0 cm and mass m = 0.880 kg. The ball and rod, initially at rest in a vertical position and free to rotate around the axis shown in the figure below, are nudged into motion. L m M (a) What is the rotational kinetic energy of the system when the ball and rod reach a horizontal position? J (b) What is the angular speed of the ball and rod when they reach a horizontal position? rad/s V(c) Vfreefall (c) What is the linear speed of the center of mass of the ball when the ball and rod reach a horizontal position? m/s (d) What is the ratio of the speed found in part (c) to the speed of a ball that falls freely through the same distance?

You find an interesting looking ball but can't tell if it's solid or hollow, so you design an experiment: The mystery ball is rolled along a horizontal surface with an initial translational speed of v= 2.7 m/s. Then the ball rolls up an incline and eventually stops after climbing up a vertical distance of h = 0.52 m, as shown in the figure. Based on your experiment, is the ball solid or hollow? Use calculations to support your answer. Assume the ball rolls without slipping. Note: you do not need to know the mass or radius of the ball to answer this problem. 1フ

A turntable 46.0 cm in diameter diameter starts from rest, and rotates at 68.0 rpm at its first complete revoļution with constant angular acceleration. If it maintains the same acceleration, a) what is the rotational speed at time 34.0 seconds? b) what is the tangential speed of a point 10 cm from the edge of the turntable at time 34.0 seconds? Enter answer "O" in the answer box. Submit in the corresponding folder (or email) your solution by 3:50 pm, include a sketch/drawing of the rotating wheel, and a step- by-step solution.

A 2.00-m long rod is hinged at one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. (a) What is the angular acceleration as it is released? (b) What is the angular acceleration when it reaches the vertical position? (c) Which position has the maximum angular velocity (vertical or horizontal)? (d) Which position has the maximum angular acceleration (vertical or horizontal)? (The moment of inertia of a rod about one end is ML2/3.)