Suppose we wrap a string around the surface of a uniform cylinder of radius 45.0

Question

Suppose we wrap a string around the surface of a uniform cylinder of radius 45.0 cm that is supported by an axle passing through its center. This cylinder rotates without friction and we tie a mass to the end of the string and let it fall under the influence of gravity. As the weight falls, we measure the constant acceleration of the falling mass to be 7.0 m/s2. Find the angular acceleration that the cylinder will experience under these conditions. (Assume the positive direction is the initial direction of rotation of the cylinder. Indicate the direction with the sign of your answer.)    

Explanation / Answer

LINEAR ACCELERATION OF EACH FALLING OBJECT IS RELATED TO ANGULAR ACCELARATION AS

angular acceleration=linear acceleration/radius of the cylinder

angular acceleration=7/0.45=15.5555 radians/sec^2

direction is clock wise where as linear acceleration is towards the earth pointing downwards

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