A thin- walled cylinder of radius 50 cm, mass 1.0 kg, is mounted on a frictionless, horizontal axle as in Figure 1 . A light cord wrapped around the wheel supports an object of mass 2 kg. When the wheel is released, the object accelerates downward, the cord unwraps off the wheel, and the wheel rotates with an angular acceleration. Find the angular acceleration of the wheel, , and the tension in the cord

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Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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A thin- walled cylinder  of radius 50 cm, mass 1.0 kg, is mounted on a frictionless, horizontal axle as in Figure 1 . A light cord wrapped around the wheel supports an object of mass 2 kg. When the wheel is released, the object accelerates downward, the cord unwraps off the wheel, and the wheel rotates with an angular acceleration. Find the angular acceleration of the wheel, , and the tension in the cord.

Expert Solution
Step 1

radius = 50 cm mass = 1 kg mass of object = 2 kg using , Tension = M (g-a) T= 2(9.8-a)T= 19.6 - 2a 

 

Step 2

Now, torque = R*F = I * angular acceleration R*(19.6 - 2a) = (1/2)(m)(R)2 *(a/R)19.6 - 2a = (1/2)(a)(a)19.6 = 2.5 aa = 7.84 m/s2angular acceleration =a/R  = 7.84/0.5 = 15.68 rad/sec2  (angular acceleration)

 

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