Sphere and Cylinder having different accelerations down a plane.

At the upper end of an inclined plane of length L, a uniform sphere is released from rest. At the same instant, a uniform cylinder is released from rest at distance d ahead of the sphere such that both sphere and cylinder arrive at the same time at the lower end of the plane. a. The distance d is what fraction of length L? b. At the instant they both reach the lower end of the plane, find the ratio of their linear velocities Vcyl/Vsph. See attachment #1 for diagram showing parameters.

Normal Force for car on incline

A 3,000 lb car is parked a an angle of 30 degrees, facing uphill. The center of mass of the car is halfway between the front and rear wheels and is 2ft above the ground. The wheels are 8ft apart. Find the normal force exerted by the road on the front wheels and the rear wheels.

Falling Stick

A uniform stick of mass M and length l is suspended horizontally with end B on the edge of a table, and the other end, A is held by hand. Point A is suddenly released. At the instant after release: a) What is the torque about B? b) What is the angular acceleration about B? c) What is the vertical acceleration of the center of mass? Answer: 3g/4 d) From part c, find by inspection the veritcal force at B. Answer: mg/4

Working with rotational motion of a mass on a string about a rod.

Mass m is attached to a post with radius R by a string. Initially, the mass is a distance r from the center of the post and is moving tangentially with a speed Vo. In case (a) the string passes through a hole in the center of the post at the top. The string is gradually shortened by drawing it through the hole. Case (b) the spring wraps around the outside of the post. Note that in both cases the mass m moves in a circular motion around the rod. What quantities are conserved in each case? Find the final speed V of the mass when it hits the post for each case?

Calculating the amount of torque required to keep a cylinder rotating in a uniform V grove.

A cylinder of mass M and radius R is rotated in a uniform V grove (which looks like a rectangular block with an 45-45-90 degree triangular prism cut from the center- that the cylinder rotates in) The cylinder has a constant angular velocity w and a coefficient of friction u with each surface. What torque must be applied to the cylinder to keep it rotating? Hint: If u=0.5, R=0.1m, W=100N then torque=5.7 Nm