Which of the following kinetic energy (KE) is available in a rolling body without slipping?

option(3)

CONCEPT:

• The kinetic energy of a body rolling without slipping is the sum of Kinetic energies of:
  • Translational Motion 
  • Rotational Motion

KE = Kinetic Energy of Translational Motion +  Kinetic Energy of Rotational Motion.

Kinetic Energy of Rotational Motion = 1/2 (Iω2) where I is a moment of Inertia and ω is called angular velocity.

EXPLANATION:

• Rolling motion can be regarded as the combination of pure rotation and pure translation. 
• So it will have both rotational as well as translational kinetic energy.
• Hence option 3 is correct.

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Additional Information

• Translational Motion: The translational velocity of the wheel or disc is the velocity vcm of its center of mass. As the center of mass of the rolling wheel lies as its geometric center C, so vcm is the velocity of C. It is parallel to the level surface.

• Rotational Motion: The wheel rotates with the angular velocity ω about its symmetry axis through C.
• The linear velocity of a particle P at a distance r from the axis due to rotational motion. 

vrot = rω (ω is called as angular velocity)

The velocity vrot  is directed perpendicular to the radius vector CP.as shown 

• The effective linear velocity v of particle P is the resultant of velocities vrot and vcm .
• It can be shown that is perpendicular to the line AP. Therefore, the line passing through the bottom of point B and parallel to the axis through C is called the instantaneous axis of rotation. 
• At the bottom point B, the linear velocity vrot , due to rotation, is directed exactly opposite to the translational velocity vcm .
• Also vrot = Rω (angular velocity) at point B. The point B will be instantaneously at rest vcm = Rω (ω is called as angular velocity)
• At the top point A of the wheel, the linear velocity Rω (angular velocity)  due to rotational motion and the translational velocity vcm are in the same direction, parallel to the level surface.