IIT JEE , AIEEE Forum - Physics , Mechanics

srujana

A sphere is rolled on a rough horizontal surface. It gradually slows down and stops.The force of friction tries to ;

decrease the linear velocity and increase the angular velocity.

plz explain how

(H.C.Verma vol 1, pg 195 q 14)

elessar_iitkgp

The above statement is true only if the cm of the sphere is given some initial velocity, and set in motion over a rough surface. Lets see how:

Initially, the cm of the sphere has some velocity, say, v₀. Then, all points of the sphere have the same velocity, as in translational motion, all points of the rigid body have same velocities.

Hence, the point of contact also has a velocity v₀. hence, the point of contact has a tendency to slip along the direction of v₀, and hence, the maximum value of friction will act to prevent it (its not motion impending, its one that will occur definitely)

Now, this friction is in opposition to v₀ and hence will decrease v₀.

However, it produces a torque and produces a torque that increases the magnitude of angular velocity.

deeplove

The case is valid if the point of contact of the body and surface moves with time.

Here we visualize the problem.

Look, the body moving and then its set on a rough surface. The friction force tries to push the surface in forward direction and hence the opposite force acts on the body in backward direction which causes the linear velocity to decrease. And since the body is a rigid body, this force causes a torque about the center of mass which causes the angular velocity.

Hence in this way the angular velocity increases and linear velocity decreases as far as the force is there. It must be noted that if this friction force is removed now, no change in either velocity will occur.

The friction force is necessary to set the body in rotational motion but once the body is sat in rotational motion, it will continue to be in the same state even if the friction force are removes.

.......................................................................................................................

GaryK

Te first part should be easy to understand(that linear velocity decreases due to friction).

To have angular velocity, an external torque must be applied.
This torque will be supplied by friction, having magnitude:

Torque = Force applied due to friction (

mg) x Radius of sphere.

Hope this helps

Ask & Discuss Questions with Community & Experts