A uniform thin rod of mass 0.3 kg and 1 meter long has a moment of 0.025 kg m^2.

Question

A uniform thin rod of mass 0.3 kg and 1 meter long has a moment of 0.025 kg m^2. There is a 0.02 kg mass attached to one end. Find: a) The angular acceleration, alpha, of the assembly immediately after release from rest b) The linear acceleration, a, of the 0.2 kg mass immediately after release from rest A rotating disk of mass 0.5 kg and radius of 0.1 m is attached to a hanging weight of light string over a light string over a light frictionless pulley. Find a) Acceleration of the box b) Angular acceleration of the disk c) Tension in the string A large pulley has an outer radius of 0.25 m. A string is wrapped around and is riding on the inner grove, which is 0.2 m from the center of the pulley. The string is attached to a 0.3 kg hanging weight. After released from rest, the weight takes 1.1 seconds to strike the floor 1.5 m below. Find: a) a of the box b) I of the pulley

Explanation / Answer

2) Here, 0.4 * 9.8 - T = 0.4a

Also, T * 0.1 = (1/2 * 0.5 * 0.12) * alpha

=>    T * 0.1 = (1/2 * 0.5 * 0.12) * (a/0.1)

=>   T   = (1/2 * 0.5) * (a)

Thus,   0.4 * 9.8 - (1/2 * 0.5) * (a) = 0.4a

=> acceleration , a = 6.03 m/s2

Thus, Tension , T = (1/2 * 0.5) * (6.03)

                 = 1.5075 N

Thus, angular acceleration =   6.03/0.1

                                             = 60.3 rad/s2

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