Rolling Friction
Get a feel for Rolling Motion and its nuances.
1) A Car Tyre rolling down a slope: The car is moving linearly in translation, whereas only the Tyre is rotating (axis of rotation being the centre point) . Also the Tyre Centre axis and the body holding the tyre does not rotate, the centre axis of the Tyre is also having a translation type of motion as the tyre moves down the slope. That’s why the axle pulls the car and the car is moving in a translation direction in a Linear way.
A close look at a ROLLING TYRE :- If radius of Tyre = R , the tyre will rotate by 2∏R , its circumference, in each rotation, and this will be the same exact LINEAR distance completed by the car as well as Tyre Centre , provided there is no slipping / skidding between the tyre and road surface.
In image below, the Tyre is moving forward in translation, hence the friction at the ground contact point , also acts in forward direction. This is correct because friction acts opposite to the direction of Tyre’s rotation. Only then the tyre will be able to move forward .
Friction direction is forward at the contact patch, for a Tyre rotating and moving forward in the direction of translation.
2) A Spherical BALL rolling and moving down a SLOPE:-
Let M= mass of ball, and g= acceleration due to gravity
There are 2 distinct motions :-
A) Rotation motion about the ball’s own axis, also its Centre of Mass (CM) in case of “Pure Rolling without Slipping”
B) Translational motion / Linear motion of the ball’s Centre of Mass (CM) along a straight line down the inclined plane
The basic principle of the Ball’s CM’s motion down the inclined plane, is similar as that of a Rectangular Block sliding down an Inclined Plane. Here too, The Centre of Mass of the Ball experiences a Force acting through its Centre of Mass, and acting downwards along the slope of the Inclined Plan, this is a component of of the gravitational force Mg acting vertically downwards through the CG of the ball. Thus the main primary force is the vertical Mg acting through the CG
Accordingly, the Frictional force between the BALL and inclined plane surface is set up, this tends to oppose the motion , frictional force acts upwards along the slope of the inclined plane. It is this Frictional Force that causes Rotational Torque on the ball. This type of motion is called “PURE ROLLING without SLIDING”
WHAT if there was zero frictional co-efficient between the ball and plane? Then the ball will slide /slip down the plane, without any rolling. This type of motion is called “SLIDING or SLIPPING”
The Ball gets a Rotational Motion due to Frictional Force (aided by Gravitational force Mg) . Thus, every particle on the Ball is rotating clockwise at every instant. Every ball or sphere has a single POINT CONTACT with the surface of inclined plane.