A uniform, solid sphere of radius 4.50 cm and mass 4.50 kg starts with a purely translational speed of 2.00 m/s at the top of an inclined plane. The surface of the incline is 1.00 m long, and is tilted at an angle of 29.0 ∘ with respect to the horizontal. Assuming the sphere rolls without slipping down the incline, calculate the sphere's final translational speed v 2 at the bottom of the ramp.

Unpolarized light of intensity i_0=750w/m^2 is incident upon two polarizers. after passing through both polarizers the intensity is i_2=280w/m^2. (a) what is the intensity of the light after it passes through the first polarizer in w/m^2? (b) write an equation for the angle between the polarizers in terms of the initial (i_0) and final (i_2) intensities. (c) find the angle between the polarizers in degrees.

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 are true about beta reactions? there will be more than one answer. a. it has no change b. it doesn't change the mass of the number c. it has a mass of 0.0005 atoms d. it causes transmutation.