PURE ROLLING AND BICYCLE MOTION

 Rolling is a beautiful example of rotational mechanics seen in our daily life. When the centre of the wheel moves linearly and the spoke rotate about its centre in it own plane the motion is known as pure rolling. Now there are three different situation when you apply a brake on bicycle. Actually during pedaling you provide a torque at the back wheel centre, as a result the wheel starts rotating about a fixed line, and the friction points in the forward direction and the centre of the wheel accelerates in forward direction , but the frame of the cycle also accelerates in the forward direction provide a force at the centre of the front wheel. The frame also provides a force at the centre of the back wheel broken into vertical and horizontal component .To make the frame accelerates forward the friction at the contact point of the back wheel pointing forward must be greater than the the backward horizontal component of this frame force. As the frame exerts a forward force on the frontthrough the wheel does not rotate as there is no torque to rotate it but it has a tendency only to translate, so the contact point also has a tendency to move forward as a result the friction point backward. Due to this backward friction at the front wheel the friction provides a clockwise angular acceleration to the wheel and it translate in the forward direction by rotating. Now also to make the acceleration of the front wheel forward the fomard horizontal force provided by the frame should be greater than the backward friction. Now to accelerate the whole frame forward the net result is that the friction at the rear wheel should be greater than the front wheel. when you apply a brake at both wheel the angular velocity of the back wheel starts decreasing but you don't decrease the linear velocity of the the wheel, so to decrease the linear velocity of the back wheel the fiction will point backward and in the similar sense the friction at the front wheel also points backward and the net force on the system acts backward and there Is no question of what friction force is greater. In the next case when you apply the brake only at the back wheel you start decreasing angular velocity of the back wheel and the friction points backward to decrease the linear velocity and the linear velocity of the whole frame is decreasing and it exerts force on the backward direction on the front wheel and decreases its linear velocity ,so to decrease the clockwise angular velocity the friction points forward, so to accelerates the CM of the system backward the friction at the rear wheel is greater than the front wheel ,the force of frame is an internal force when we considered total as a system. The other case when you apply brake only at the front wheel is also can be similarly verified. Now the case is different when we talk about the rolling Sphere. The forces acting on the sphere at any instant are weight, friction at contact, normal reaction of surface. When the centre of the sphere de accelerate forward the friction points backward which produces a clockwise angular acceleration, so then how could the sphere stops? Here actually the contact is not at a particular point rather a area of contact and as a result the normal force shifts slightly rightwards to give a anticlockwise angular acceleration to stop it.