1.Evaluate the moment of inertia of a spherical shell of mass M,radius R,and thickness t.(15%,Show detail of your calculations) 2.in one of the regular game of MLB,Chien-Ming Wang,a famous pitcher of New York Yankee from Taiwan,throw a "Sinkling Fastball" with a speed of 94mile/h (or 150km/h).The ball falls rapidly with a little deflection to the right batter near the home plate.If the ball rotates with angular velocity 200rad/s,the radius the ball is 3.6cm and the density of the air is 1km/m^3 as showed in the figure 1, (a)what is the different of the pressure between the top side and bottom side of the ball? (b)what is the distance the ball(150g) would drop due to the pressure as the ball go through the region near the home plate(about 2m)?(15%) 3.A puck of mass m slides with velocity v0 on a horizontal frictionless surface as shown in figure 2.Lying on the surface at rest is a dumbbell formed by two other pucks,one with mass m and the other with 2m,joined by a massless rod of length L.The axis of the dumbbell is inclined at 30度 with respect to v0 as shown.The moving puck collides and sticks to the lighter end of the dumbbell. The kinetic energy(translation and rotation) of the system after the collision is?(15%) 4.Two circular hoops,X and Y,are hanging from nails fixed on the wall.The mass of X is four-times that of Y,and the diameter of X is also four times that of Y.If the period of small oscillations of X is T,what is the period of small oscillation of Y?(10%) 5.Two springs S1 and S2 have negligible masses and the spring constant of S1 is 1/3 that of S2.When a block is hung from the springs as shown in the figure 3 and spring come to equilibrium again,the ratio of the work done in stretching S1 to the work done in stretching S2 is?(10%) 6.A satellite's orbit depends on its total energy. (a)Find the total energy of the satellite in a circular orbit. (b)If the kinetic energy of the satellite is halved,what is the minimum speed of the satellite. Assume that M and m are the masses of Earth and the satellite.(10%) 7.In figure 4,a ball of 1.5kg is connected by means of two massless strings, each of length L=2.0m,to a vertical rotational rod.The strings are tied to the rod with separation d=1.2m and taut.The tension in the upper string is 40N.What are (a)the tension in the lower string (b)the magnitude of the net force F(net) action on the ball (c)the speed of the ball? (15%) 8.A block of 300g is dropped onto a relaxed vertical spring that has a spring constant of k=2N/cm as showm in figure 5.The block becomes attached to the spring and compresses the spring 15cm before momentarily stopping.While the spring is being compressed, (a)What work is done on the block by the spring force? (b)If the speed at impact is doubled,what is the maximum compressoion of the spring (10%) -- be excellent and important reader --

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