A rolling body undergoes simultaneous rotational and translational motion. Friction is required to start rolling. Rolling without slipping is known as “pure rolling”. When the wheels roll without slipping, at any instant of time, the point of the wheel in contact with the surface is instantaneously at rest with respect to the surface. No static frictional force acts on the wheels when they are in pure rotation.
When a body like the wheel is in rolling motion, different particles of the body will experience different velocities. Let us study this by considering a disc of radius R rolling on a flat surface without slipping.
This is the condition for pure rolling: For any rolling body, if VCM = ωR, then it rolls without slipping. If VCM < ωR, the rolling object has some backward slipping and the rolling is called “rolling with backward slipping”. If VCM > ωR, the rolling is called “rolling with forward slipping”.
Consider the rotational motion of the disc about its centre of mass. The torques about the centre of mass due to the weight and normal force are zero as the lines of action of these forces pass through the centre of mass. Only the torque about the centre of mass due to the frictional force can cause rotational motion in the disc.
M → Mass ot ine aisc
VCM → Velocity of the centre of mass
Kinetic energy of the centre of mass
"I" → Moment of inertia
"ω" Angular velocity
Rotational kinetic energy
When a system of particles exhibits simultaneous translational and rotational motion the kinetic energy of a system of particles, KE, can be written as the sum of the kinetic energy of the centre of mass, KCM, and the rotational kinetic energy of the system of particles about its centre of mass, Kr.
KE = KCM + Kr = ½ MVCM2 + ½ Iω2
While solving problems relating to the rolling of an object on an inclined surface, we can use two different methods. In the first method, we analyse the forces and torques acting on the object. The second method involves the use of the Law of Conservation of Energy.