Kinetic Energy of Rolling Motion
The kinetic energy of a rolling body can be divided into two types i.e.,
- Translational Kinetic Energy
- Rotational Kinetic Energy
The kinetic energy of a system of particles (K) can be divided into the kinetic energy of centre-of-mass motion (translation) (MV2/2) and the kinetic energy of rotational motion about the system’s centre of mass (K′). Therefore the total kinetic energy of the system is,
K = K‘ + (MV2)/2
The kinetic energy of the rolling body’s centre of mass, i.e., the kinetic energy of translation, is m(vcm)2/2, where m is the body’s mass and vcm is the centre of mass velocity.
The motion of the rolling body about its centre of mass K′ is the kinetic energy of rotation of the body
K′ = (Iω2)/2
where I is the moment of inertia about the suitable axis, which is the rolling body’s symmetry axis.
Therefore, the kinetic energy of a rolling body is given by
K = (Iω2)/2 + [m(vcm)]2/2
Substitute I = mk2 where k is the corresponding radius of a rapidly moving body and ω=vcm/R where R is the radius of the circular moving body.
[Tex]K=\frac{1}{2}\frac{ mk^2v_{cm}^2}{R}+\frac{1}{2}mv_{cm}^2\\ K=\frac{1}{2}mv_{cm}^2\left(\frac{k^2}{R^2}+1\right) [/Tex]
Rolling Motion
Rolling motion is one of the most relevant movements we can see in our everyday life. There is a rolling motion in all wheels used in transportation like cars, buses, trains, aero planes, bikes, and buffalo carts. We can also see the rolling motion in gears and ball bearings. In this article, we will learn about the basic fundaments of Rolling Motion like definition, examples, and its applications in the real world. So, let’s start learning the fundamental topic of Rolling Motion.
Table of Content
- Rolling Motion Definition
- Formulas for Rolling Motion
- Kinetic Energy of Rolling Motion
- Types of Motion of a Rigid Body on an Inclined Plane
- Sliding of Block on Inclined Plane
- Rolling of Cylinder on Inclined Plane
- Rolling Friction
- Formula for Rolling Friction
- Applications of Rolling Motion
- Sample Problems on Rolling Motion