The ropes in the figure below are each wrapped around a cylinder, and the two cy
ID: 1978778 • Letter: T
Question
The ropes in the figure below are each wrapped around a cylinder, and the two cylinders are
fastened together. The smaller cylinder has a diameter of 10 cm and a mass of 5.0 kg; the larger
cylinder has a diameter of 20 cm and a mass of 20 kg. What is the angular acceleration of the
cylinders? Assume that the cylinders turn on a frictionless axle.
Explanation / Answer
torque about cylinder 1 = 4 * 9.8 * .1 = 3.92 N (for no rotation) torque about cylinder 2 = 2.5 * 9.8 * .2 = 4.9 N will get counter clockwise rotation 2.5 * a1 = 2.5 * 9.8 - T1 where T1 is tension in rope 1 (I) 4.5 * a2 = T2 - 4 * 9.8 where T2 is tension in rope 2 (II) T1 * .2 - T2 * .1 = I * alpha where alpha = angular acceleration (III) a1 = alpha * .2 and a2 = alpha * .1 (IV) I = 1/2 * 5 * .1^2 + 1/2 * 20 * .2^2 = .425 kg-m^2 a1 = 2 a2 from (IV) Now just begin eliminating variables (I'll) get timed out! Also a1 = alpha * .2 and a2 = alpha * .1
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