### Compute the rotational inertia of the pulley

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##### Reference no: EM1386869

Q. A solid disk of unknown mass and known radius R is used as a pulley in a lab experiment, as shown above. A small block of mass m is attached to a string, the other end of which is attached to the pulley and wrapped around it several times. The block is mass m is free from rest and takes a time t to fall the distance D to the floor.

(a.) Compute the linear acceleration a of the falling block in terms of the given quantities.
(b.) The time t is measured for various heights D and the data are recorded in the following table. D (m) = 0.5, 1, 1.5, 2, and the corresponding times are t(s) = .68, 1.02, 1.19, 1.38
(i) what quantities must be graphed in order to best determine acceleration of the block? Describe your reasoning.
(ii.) On the grid below, plot the quantities determined in b. i., label the axes, and Illustrate the best fit line to your data.
(iii.) Use your graph to compute the magnitude of the acceleration.
(c.) Compute the rotational inertia of the pulley in terms of m, R, a, and fundamental constants.
(d.) The value of acceleration found in (b)iii, along with numerical values for the given quantities and your answer to (c), can be used to determine the rotational inertia of the pulley. The pulley is removed from its support and its rotational inertia is found to be greater than this value. Give an explanation for this discrepancy.

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