A solid uniform sphere resting on a rough horizontal plane is given a horizontal impulse directed through its center so that it starts sliding with an initial velocity $v_0$. When it finally starts rolling without slipping the speed of its center is
So, angular momentum will remain conserved along point of contact By conservation of angular momentum Angular momentum will remain conserved along point of contact $I \omega=$ constant $ m v_{0} r =m v r+\frac{2}{5} m r^{2} \times \omega\,\,\, \left(\because \omega=\frac{v}{r}\right) $ $ m v_{0} r =m v r+\frac{2}{5} m r^{2}\left(\frac{v}{r}\right) $ $v_{0} =v+\frac{2}{5} v $ $ v_{0} =\frac{7}{5} v $ $\Rightarrow v=\frac{5}{7} v_{0} $
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Top Questions on System of Particles & Rotational Motion
The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.
