Problem Set Homework 5 1. Calculate the moment of inertia I for the following objects: a. A rod of length L with density
   and axis of rotation in the center of the rod.   0 is define to be at the center of the rod. b. A solid disc of radius R with axis of rotation at its center and density
    2. A uniform solid ball has a few turns of light string wound around it. if the end of the string is held steady and the ball is allowed to fall under gravity, what is the acceleration of the center of the ball? (assume the string remains vertical) 3. Find the period of a physical pendulum with the following shapes: (Hints: The moment of inertia for two objects attached to each other can be calculated by individually calculating their moments of inertia and adding them together. You will need to use the parallel axis theorem in this problem.) a. A thin rod of length L and mass m with a solid disc of radius L/4 and mass m centered at the end. The axis of rotation is at the end of the rod opposite the solid disc. b. A thin rod of length L and mass m with a hoop of radius L/4 and mass m centered at the end. The axis of rotation is at the end of the rod opposite the hoop. c. Which shape has the larger period? Explain why your answer makes sense conceptually. 4. Sarah is riding on the carousel. The carousel rotates clockwise when viewed from above. The carousel is coming to a stop, so it is slowing down. Sarah is in the northwest quadrant. a. Draw vectors for , , and ′ when the carousel is viewed from above. b. Use the right hand rule to determine the directions of the transverse force and the centrifugal force. c. Use formal vector calculations to determine the directions of the transverse force and the centrifugal force. d. Do your answers for (b) and (c) agree? Explain why your answers make sense conceptually. 5. Suppose you set up the kiddy pool experiment as conducted in Veritasium and SmarterEveryDay. You set up your kiddy pool in Commerce, which is at a latitude of 33° N. You have a friend in Mexico City, which is at a latitude of 19° N. a. In which city would you expect the Coriolis force to be stronger? Explain your reasoning. (Hint: The component of the velocity which is perpendicular to  varies with latitude.) b. Is the centrifugal force from the Earth’s rotation larger for you or your friend? Explain your reasoning. (Hint: ′ varies with latitude.)
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