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.

 

[kerimek]

I understand your confusion. It is important to clarify the definitions of rolling and sliding in this context. Rolling refers to the motion of an object where it rotates about its own axis while also translating without slipping. Sliding refers to the motion of an object where it translates without any rotation.

In this scenario, the hula hoop has an initial velocity Vsliding, which means it is only sliding without any rolling. When it encounters the rough area, it will experience a frictional force that will cause it to start rotating about its own axis while also continuing to translate. This means the hoop will be both rotating and sliding at the same time.

To distinguish between the different types of motion, you can look at the velocity of the hoop. If the velocity is purely translational, then it is only sliding. If the velocity is purely rotational, then it is only rolling. If the velocity has both translational and rotational components, then it is sliding with rolling.

In this scenario, the hoop will eventually reach a point where the frictional force is strong enough to cause it to roll without slipping. This means the velocity will have both translational and rotational components, but the hoop will not be sliding anymore.

I hope this helps to clarify the concept of rotational kinematics and the different types of motion that can occur. Remember, as a scientist, it is important to always question and seek clarification when faced with confusion.