A solid, uniform, spherical boulder (I= 2/5 MR2) starts from rest and rolls down a 50 m hill, as shown at the figure at the right. The top half of the hill is rough enough to cause the boulder to roll without slipping, but the lower half is covered with ice and there is no friction. What is the translational speed of the boulder when it reaches the bottom of the hill

A potter's wheel, with rotational inertia 12 kg-m², is spinning freely at 40 rpm. The potter drops a lump of clay onto the wheel, where it sticks a distance 1.2 m from the rotational axis. If the subsequent angular speed of the wheel and clay is 32 rpm what is the mass of the clay? 1.4 kg 2.3 kg 1.8 kg O 2.1 kg

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.…

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