Rolling and Newton’s first law
A pure rolling is equivalent to pure translation and pure rotation. It, therefore, follows that a uniform rolling (i.e. rolling with constant velocity) is equivalent to uniform translation (constant linear velocity) and uniform rotation (constant angular velocity).
According to Newton’s first law for translation, if net external force is zero, then translation of the object i.e. linear velocity remains same. Similarly, according to Newton’s first law for rotation, if net external torque is zero, then rotation of the object i.e. angular velocity remains same. It means, then, that a body in uniform rolling motion shall roll with the same velocity. I like to share this Projectile Motion Equation with you all through my article.
Note here that when we say that a body is rolling with a constant velocity, then we implicitly mean that it is translating at constant linear velocity and rotating at constant angular velocity. It is so because two motions are tied to each other with the following relation,
vC = ωR
We had difficulty to visualize a real time situation to verify Newton’s first law in translation or rotation, as it was difficult to realize a “force – free” environment. However, we reconciled to the Newton’s first law as we experienced that a body actually moved a longer distance on a smooth surface and a body rotated longer without any external aid about an axle having negligible friction and resistance. In the case of rolling also, we need to extend visualization for the condition of rolling when neither there is net force nor there is net torque.
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One such possible set up could be a smooth horizontal plane. If a rolling body is transitioned (i.e. released) on a smooth plane with pure rolling at certain velocity, then the body will keep rolling with same velocity. This statement, if we agree, can be construed to be the statement of Newton’s first law for pure rolling motion.
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