Suppose we wrap a string around the surface of a uniform cylinder of radius 40.0

Question

Suppose we wrap a string around the surface of a uniform cylinder of radius 40.0 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 4.0 m/s^2. 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.) Suppose we wrap a string around the surface of a uniform cylinder that s 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 t fall under the influence of gravity. If the mass is 3.0 kg, find the tension in the rope as the mass is falling with an acceleration of 3.0 m/s^2.

Explanation / Answer

Net force acting on hanging body, Fnet = m*g - T

m*a = m*g - T

T = m*g - m*a

= 1.7*9.8 - 1.7*3

= 11.56 N <<<<<<-----------Answer

we know, a_tan = r*alfa (here r is radius and alfa is angular acceleration)

==> alfa = a_tan/r

= 3/0.34

= 8.82 rad/s^2 <<<<<<-----------Answer

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