A solid ball of mass m = 500 g hangs from a string attached to a rigid support p

Question

A solid ball of mass m = 500 g hangs from a string attached to a rigid support point on the ceiling to form a pendulum. The string is L = 0.5 m. If this pendulum is considered ideal (a point mass on a massless string released from a small angle), what angular frequency does it oscillate with What is the magnitude of the torque due to gravity on this idealized mass about its support point when lifted out to 20 degree What is the magnitude of the torque due to the tension on this idealized mass about its support point when lifted out to 20 degree What kind of energy does the mass have when at it swings through its lowest point-translational or rotational kinetic energy Explain your answer. Now let's see how much the idealized approximations affect our results by treating the system as a physical pendulum where the mass is distributed. Find the actual moment of inertia of the ball-on-the-string system about the pivot by assuming the following: The total combined mass of the ball and string is still m. 90% of the mass is in the ball and 10% is in the string. The string has a length L. The ball's center of mass is still located a distance L away from the pivot. The ball has a radius of L/10. You may use moments of inertia from the text (p. 318). Find the actual angular frequency of the system for small amplitudes. Give your answer in terms of omega_0, the frequency you found in part a. (We make these approximations because they don't make a huge difference-your answer will be nearly the same as omega_0. Be sure to be precise enough to show the real difference in frequency.) Given the actual angular frequency you found in part f, explain why it makes sense.

Explanation / Answer

b.

Torque = force x perpendicular distance
=>T = mg x d sinA
=>T = 500g x 9.8 x 0.5 x sin20o
=>T = 0.5 x 9.8 x 0.5 x 0.912 = 2.2344 N-m

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