A Round Uniform Body Of Radius R, Mass M And Moment Of Inertia I Rolls Down (Without Slipping) An Inclined Plane Making An Angle θ With The Horizontal. Then Its Acceleration Is

Sol:

v = rw

a =?

\( mgsin\Theta – F = ma —-[1] \) \( F(R) = I \alpha R—-[2] \)

Therefore, \( a = \alpha R—-[3] \) \( mgsin\Theta = ma + \frac{I\alpha}{R} \) \( \Rightarrow ma + \frac{I\alpha}{R^{2}} \)

Therefore, \( a = \frac{mgsin\Theta }{m + \frac{I}{R^{2}}} \) \( \Rightarrow \frac{gsin\Theta }{1 + \frac{I}{MR^{2}}} \)

Therefore, its acceleration is \( \frac{gsin\Theta }{1 + \frac{I}{MR^{2}}} \)

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