recitation08-solutions - Physics 2750‐ Recitation 08 1 A...

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Unformatted text preview: Physics 2750‐ Recitation 08 1. A uniform hollow disk has two pieces of thin light wire wrapped around its outer rim and is supported from the ceiling. Suddenly one of the wires breaks, and the remaining wire does not slip as the disk rolls down. Find the speed of the center of this disk after it has fallen a distance of 1.2 m. Problem 1 Problem 2 2. A uniform solid cylinder of mass M is supported on a ramp that rises at an angle θ above the horizontal by a wire that is wrapped around its rim and pulls on it tangentially parallel to the ramp. A) Show that there must be friction on the surface for the cylinder to balance this way. B) Find this friction force. 3. A uniform rod of length L and mass M is free to rotate on a frictionless pin through one end. The rod is released from rest in the horizontal position. A) What is the angular speed of the rod at its lowest position? B) Determine the tangential speed of the center of mass and the tangential speed of the lowest point on the rod in the vertical position. The moment of inertia for the rod with respect to the pivot point is 1/3 ML2. 4. A projectile of mass m = 0.1 kg moves to the right with speed v = 2 m/s. The projectile strikes and sticks to the end of a stationary rod of mass M = 0.5 kg and length d = 1 m that is pivoted about a frictionless axle through its center (a) Find the angular speed of the system right after the collision. (b) Determine the change in kinetic energy due to the collision. Problem 4 Problem 5 5. A solid sphere of radius R and mass M starts rolling from rest, without slipping, from the top of an inclined plane of angle θ. A) Find the linear speed (the speed of its center of mass) at the bottom of the inclined plane, and B) determine the magnitude of the linear (translational) acceleration of the center of mass. ...
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