Hello dear we have already learnt about the concept of rotational motion, moment of inertia etc. The kinetic energy of rotating body is given as,
Where ‘I’ is moment of inertia of body and be the angular velocity of rotating body.
In this article we are going to discuss about the rolling motion of body, so let’s learn the concept in detail.
Let’s discuss the concept of rolling motion……………!
Rolling Motion:-
The rolling motion of a body is combination of translational motion and rotational motion. Thus the kinetic energy of rolling body is the sum of translational kinetic energy and rotational kinetic energy given as,
Rolling Motion of body from plane horizontal surface
Let M=be the mass of spherical ball.
R=Radius of sphere
K= Radius of gyration of sphere
I= Moment of inertia of sphere
ω=angular velocity of rotation of sphere
According to the statement, rolling motion is combination of translational kinetic energy and rotational kinetic energy, and then the kinetic energy of rolling motion is given as,
Rolling motion of a body without slipping on an inclined plane:
Consider a rigid body of mass ‘M’ and radius ‘R’ rolling down inclined plane of inclination ‘θ’ from height ‘h’ shown in a fig. below.
Body starts from rest and rolls down, it loses its gravitational potential energy. This potential energy is converted into kinetic energy.
If ‘V’ is the linear speed acquired by the body when it reaches the bottom of the inclined plane, then loss in potential energy = gain in kinetic energy.
Let ‘a’ be the linear acceleration of the body while rolling down the plane and ‘S’ is the length of the plane.
As the body starts forms rest, u = 0
v2 = 0 + 2as
This value changes with different geometrical shapes.
Some special conditions…….!
1.) For ring,
Radius of gyration= Radius of ring
i.e. k=R