Mame: Period: 3. The student sets up a third experiment, constructing a yo-yo out of a disk and a string wound around the circumference. The string is fixed to a support and the yo-yo is released from rest. The yo-yo has mass m, radius R, and rotational inertia about its center equal to (1/4) mR2. a) Draw a free-body diagram for the yo-yo once released and h derive an expression for its linear acceleration in terms of m and/or g. b) Derive an expression for the linear speed of the yo-yo's center of mass after it has descended from its release point a distance h, in terms of m, g, and/or h. c) A new yo-yo design has exactly the same mass and radius as the original, but the steel part is on the outer part of the yo-yo as shown. If the experiment were repeated with the new design, would the fnear speed after falling the same distance be more, less, or the same as before? Explain. 4. The student creates a fourth experiment to investigate oscillation. They suspend a bowling ball from a rope attached to the ceiling, creating a simple pendulum. The ball has a mass of 10 kg and the I rope has length 2.25 m. It starts from its lowest point and is given a : shove with initial velocity 0.45 m/s. Assume small angle oscillations. I 0 I I a) Use the period and w,__, to sketch a graph of the pendulum's angular velocity over time. m = b) On the graph above, sketch a second curve that shows the angular velocity over time if the same pendulum were released from a greater amplitude. Explain. c) Measuring the length and period T of the pendulum and knowing the radius of the earth R, this experiment can be used to determine the mass of the earth, M. Derive an expression for the mass of the earth in terms of , T, R, and G