Your professor has put 5 objects near the top of an inclined plane: a uniform density solid sphere, a hollow sphere, a hollow cylinder, a special solid cylinder in which the density is proportional to the radius (rho(r) = αr), and a solid cube. The spheres and cylinders have radius R and will roll down the plane, while the cube has sides of length 2R and a frictionless coating, so it will slide down the plane. All objects are released at the same time. Which is the last to get to the bottom of the plane?

5submission this assignment is worth 20 points total. you are required to submit the following by next lab: 1. (3 points) determine the equation for the output angular velocity ω2 = θ˙ 2 as a function of θ1, ω1 = θ˙ 1 and α. you must show all your work to receive credit. 2. (2 points) use the result of problem#1 to plot ω2 over 0 ≤ θ1 ≤ 360deg with ω1 = 360deg/sec. do this for α = {10,30}deg. show the results on the same plot and properly label the axes, title, legend. for this you can use matlab or ms excel. 3. (3 points) determine the equation for the output angular acceleration ω˙ 2 and create a plot similar to the one in problem#2. 4. (10 points) submit plots of the results (ω2 and ω˙ 2) obtained from creo/mechanism and compare them to results of problem#2 and problem#3. note that you should do these comparisons for the two cases with α = {10,30}deg. 5. (2 points) provide a brief explanation of the results. did they match? what are the implications as misalignment angle increases?

Which notation is used to represent an alpha particle? a. b. c. d.

Suppose a wire with a current is pushed upward by a magnetic field. how would the wire move if the direction of the current reversed? explain your answer.