One of the most common faced by a student while trying to solve a problem that involves rolling and friction simultaneously is to identify the direction of the frictional force. The difficulty arises from the fact that sometimes rolling friction can be deceptive to intuition. In this article, we will see various cases of rolling friction and analyze the direction of the frictional forces and the role they play in the process of rolling.
Firstly let us consider what determines the direction of friction before we look at various types of motion that involve friction and rolling. As we might already know, frictional force is a contact force and that it always opposes the direction of the motion. Therefore, even in the case of rolling the frictional force exists only between at the point of contact between the body that is in motion (in this case rolling motion) and the surface. If the point of contact is moving to the right relative to the surface, the frictional force acts to the left and vice versa. When it comes to rolling motion, the two important velocities that need to be taken into consideration are the velocity of the center of the rolling body and the velocity at the point of contact. The equality or inequality in the magnitudes of these velocities is what determines the direction of the rolling motion. Let’s see how.
Pure rolling: In the case of pure rolling the velocity of the center of mass of the body is equal to the velocity of the point of contact. This means, there is no relative motion between the ground and the point of contact. As long as there is no relative motion the possibility of kinetic friction existing between the two surfaces is zero. Only static friction exits.
Rolling with slipping: In this case, let us consider a wheel. If the velocity of the center of mass of the wheel is more than that of the velocity of the surface of the wheel, it means that the wheel has a greater tendency to translate than to rotate. Mathematically this condition can be written as Vcm > R ?. ? is the angular velocity of the body, a quantity we learnt during our Physics tuition classes in the chapters of Circular Motion and Oscillations.
In this case, the frictional force acts in the backward direction or against slipping. This case can be observed in the case of a billiard ball which moves faster but does not rotate as fast causing it to slip. The second case in rolling with slipping is when the velocity of the center of mass of the body is less that of the velocity of the point of contact. Mathematically, Vcm < R ? . In this case the body is rotating faster than it is translating and hence the direction of friction will be in the direction of the translatory motion or against the direction of rotation. This phenomenon can be observed in the beginning of a car race where the cars have high torque or angular velocity but do not more before the green lights and hence have no linear velocity called “burn out”.
Vcm – velocity of the center of mass of the body
R – Radius of the body
? – Angular velocity of the body with respect to the center of mass