Advanced Physics THP#4 Rotational Dynamics point mass m = 1kg ...

Advanced Physics THP#4 Rotational DynamicsThese problems are open book and open notes. You may not consult or confer with anyone other thanMr. Burns. Full credit will be awarded for each problem only if the correct answer is accompanied bysufficient work that is presented in such a manner that the logic and mathematical operations are clearand easy to follow. All answers must be boxed, labeled and accompanied by the appropriate units.frictionless hingeuniform rodM =10 kgL = 2 mmassless stringpoint massm = 1kg0.5 m1. (10) A 10 kg uniform rod with a length of 2 meters is connected to a frictionless hinge. Therod is released from rest and it swings down and strikes a 1 kg point mass (initially at rest) thathangs from the ceiling at a point that is 0.5 m from the end of the rod.a. Calculate the initial angular acceleration of the rod. (I rod = 1 / 3 ML 2 ).b. Find the angular acceleration of the rod when the rod is at a 36.87° angle relative to its startingpoint (below horizontal).c. Find the angular speed of the rod just before impact.d. The angular speed of the rod after impact is 1 rad/sec. Find the linear speed of the point massafter impact.

2. (10) A space shuttle astronaut in circular orbitaround the Earth has an assembly consisting of two smalldense spheres (pt. masses) each of mass M, whose centersare connected by a rigid rod of length L, and negligiblemass. The astronaut also has a device that will launch asmall lump of clay of mass M at speed v 0 . Express youranswers in terms of M, v 0 , L and fundamental constants.MLMv 0Initially the assembly is “floating” freely at rest relative tothe cabin. The astronaut launches the clay lump so that itperpendicularly strikes and sticks to one of the spheres ofthe assembly.Ma. (2) Determine the distance from the left end of the rod to the center of mass of thesystem (assembly and clay lump) immediately after the collision. (Assume that the radii of the spheresand the clay lump are much smaller than the separation of the spheres.)b. (1) On the figure above, indicate the direction of motion of the center of massimmediately after the collision. (Hint: Momentum is a vector quantity.)c. (2) Determine the linear speed of the center of mass immediately after the collision.d. (3) Determine the angular speed of the system (assembly and clay lump) around(relative to) the center of mass immediately after the collision.e. (2) Determine the change in kinetic energy as a result of the collision.3. (10) A massless rope is wrapped around a 30 kg turntable (I = 3.75 kg-m 2 ) that is free to spinon a frictionless axle. The rope passes over an ideal pulley and is attached to a 10 kg mass. The systemis released from rest.a. (1) The tension in the rope is less than 100 N. Why?b. (3) Determine linear acceleration of the mass.c. (1) Determine the angular acceleration, α, of the turntable.d. (2) The rope detaches from the turntable after 5 seconds. Find the final angular speed, ω, ofthe table.e. (3) A 4 kg lump of clay (a point mass) is now dropped (straight down) onto the turntable ata point halfway between the center and the edge of the turntable. Calculate the new angular speed ofthe turntable.M (turntable) = 30 kgR = 0.5 mmassless ropeidealpulleyfrictionless axle10 kg