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What is Dimensional Formula of Rotational Kinetic Energy?

Rotational Kinetic Energy can be defined as the kinetic energy associated with rotational motion of an object.  kinetic energy = 1/2 (mv2)  we all know that every particle in an object has same angular speed ω, and tangential speed depends on the distance r from the axis of rotation. Total kinetic Energy of rotating object is the sum of kinetic energy of all individual particles of an object.

so Rotational kinetic energy (KR) = 1/2 (mv2) = 1/2  (m r2 ω2) = 1/2 ( m r2) ω2.

We can also write it as KR = 1/2 Iω2.——- (Moment of Inertia (I)= ∑ m r2 ).

Rotational kinetic energy (KR) = 1/2 Iω2

Mathematically.

Rotational kinetic energy (KR) = 1/2 (Moment of Inertia x (Angular velocity)2)

Now we know,

Dimensional Formula of Moment of Inertia= M1L2T0
Dimensional Formula of Angular Velocity = M0L0T-1

Putting these values in above equation we get

So Dimensional Formula of Rotational kinetic energy = M1L2T-2
SI unit of Rotational kinetic energy is Joule (J).

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What is Dimensional Formula of Surface Potential?

Surface Potential  is defined as work done per unit mass.

Mathematically,
Surface Potential = Work / Mass

Dimensional Formula of Work= M1L2T-2
Dimensional Formula of Mass= M1L0T0

Putting this value in the above equation we get,

Dimensional Formula of Surface Potential= M0L2T-2
SI unit of Surface Potential is m2s-2.

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What is Dimensional Formula of Refractive Index?

Refractive Index is defined as the relative speed at which light moves through a material with respect to its speed  in vacuum.

Mathematically,
Refractive Index (n) = speed of light in a vacuum (c) /speed of light in a medium (v)

As both the values belong to same  quantity (speed), units gets nullified. So Refractive Index is dimensionless quantity.

Dimensional Formula of Refractive Index= M0L0T0.
Refractive Index is dimensionless quantity.

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What is Dimensional Formula of Specific volume?

Specific volume is defined as volume per unit mass of fluid. Specific volume is reciprocal of mass density.

Mathematically,
Specific volume = volume of fluid / mass of fluid.

Dimensional formula of volume = M0L3T0
Dimensional formula of mass = M1L0T0

Putting this value in the above equation we get,

Dimensional Formula of Specific volume= M-1L3T0.
SI unit of Specific volume  is m3/kg .

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What is Dimensional Formula of Kinetic Energy?

Kinetic energy can be defined as the energy possessed by the body by virtue of its motion.

Mathematically,
Kinetic energy (K.E) = 1/2 [Mass (m) X Velocity (v)2]

Dimensional formula of  Mass = M1L0T0
Dimensional formula of velocity= M0L1T-1

Putting the values in the above equation we get,

Dimensional formula of Kinetic energy (K.E) = M1L0T0 X ( M0L1T-1)2

Dimensional formula of Kinetic energy (K.E) = M1L0T0 X M0L2T-2

Dimensional Formula of Kinetic energy= M1L2T-2.
SI unit of Kinetic energy is Joule (J).

Note : In the above equation ½  is a constant and  constants do not affect the dimensional formula of any quantity.

posted in Dimensional Formulae | 12 Comments