Rotational Kinematics (Rolling and sliding)

[nahanksh]

Homework Statement

http://online.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/oldexams/exam3/sp08/fig23.gif
A child sends a hula hoop (moment of inertia I = MR^2) sliding without rolling across a smooth floor. The hoop has an initial velocity Vsliding. The hoop encounters a rough area where the (finite) coefficient of kinetic friction between the hoop and the floor is μK. After moving a few feet, the hoop is found to be rolling without slipping with a translational velocity Vrolling.

Immediately after the hoop enters the rough area, it is both rotating and sliding.
(True/False)

Homework Equations

The Attempt at a Solution

I thought immediately after the hoop enters the rough area, it ONLY slides and then it rotates( I thought of it like this because there was a FRICTIONLESS surface before it goes into the frictional surface..)

How can i distinguish either it 1)only rolls 2)only slides 3)slides with rolling...

It's really confusing..

Please could someone help me out?

 

[aim1732]

You can differentiate b/w rolling(pure) and sliding by relating angular and translational velocities. When the hoop slides there is no angular velocity and hence sliding.

When the hoop enters the rough area there is torque of friction that slows the centre of mass of the hoop and increases the angular velocity(impure rolling).
For pure rolling velocity of centre of mass is the product of radius and angular velocity. You can try using the kinematical equations to cover these cases.