A mass m is allowed to roll down inclined plane ( theta ). If the vertical height is h, find

i) acceleration along the inclined plane
ii) velocity  down the plane
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$$\begin{gathered} When body rolls down along the inclined plane then \\ net force acting on it: \\ f= mg\sin \theta -F \\ where F is the frictional force \\ torque = F\times r=I\alpha =Ia/r \\ where a is the acceleration \\ F= \frac{Ia}{r^2} \\ ma= mg\sin \theta -\frac{Ia}{r^2} \\ a=\frac{mg\sin \theta }{m+I/r^2} \\ where I is the moment of inertia which is different for different body. \\ when body roles down, \\ total energy will remains conserved: \\ hence \\ \frac{1}{2}I{\omega }^2+\frac{1}{2}m{v}^2=mgh \\ where \omega is the angular frequency of the objecty. \\ velocity can be calculated u\sin g this formula when shape of the object is given. \end{gathered}$$

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