A bit of mud stuck to a bicycle's front wheel of radius r detaches and is flung horizontally forward when it is at the top of the wheel. The bicycle is moving forward at a speed v and it is rolling without slipping. The horizontal distance travelled by the mud after detaching from the wheel is:

A wheel of radius R rolls without slipping on a horizontal ground. The distance travelled by a point on the rim in one complete rotation is:

An inextensible rope tied to the axle of a wheel of mass m and radius r is pulled in the horizontal direction in the plane of the wheel. The wheel rolls without jumping over a grid consisting of parallel horizontal rods arranged at a distance 1 from one another (1 lt r) . Determine the average tension T of the rope at which the wheel moves at a constant velocity v, assuming the mass of the wheel to be concentrated at its axle.

A cord is wound around the circumference of wheel of radius r. The axis of the wheel is horizontal and MI is I . A weight mg is attached to the end of the cord and falls from rest. After falling through a distance h, the angular velocity of the wheel will be

When a bicycle moves in the forward direction what is the direction of the frictional force in the rear and front wheels