
Find dimension of moment of inertia. Is moment of inertia a vector or a scalar?
Answer
491.4k+ views
Hint
To find the dimension of moment of inertia, we need to use the formula for the moment of inertia to find its units. From the dimensions of the various terms in the formula of moment of inertia, we get the dimension of moment of inertia.
Formula Used: In this solution we will be using the following formula,
where is the moment of inertia
in the mass of the body
is the radius of gyration.
Complete step by step answer
The moment of inertia of a body is its ability to resist angular acceleration. It determines the amount of torque that a body needs for a desired angular acceleration about a rotational axis. The moment of inertia of a body is given by the sum of the moments of inertia of each particle, and for each particle the moment of inertia is the product of the mass and square of the distance of the particle from the rotational axis.
Therefore we can write the moment of inertia as,
Now mass has a unit of length. So we can write the dimension of mass as,
The radius of gyration is the unit length. So we can write the radius as,
So the moment of inertia has a dimension of,
We can write this as,
So the dimension of moment of inertia can be calculated as .
The moment of inertia is the rotational equivalent of mass in the translational motion.
Now since mass is a scalar quantity, so the moment of inertia is also a scalar quantity.
Note
The dimensional formula is an equation which gives the relation between the fundamental units and the derived units in the terms of dimensions. In mechanics we take the length, mass and time as the three fundamental dimensions and they are represented by , and .
To find the dimension of moment of inertia, we need to use the formula for the moment of inertia to find its units. From the dimensions of the various terms in the formula of moment of inertia, we get the dimension of moment of inertia.
Formula Used: In this solution we will be using the following formula,
where
Complete step by step answer
The moment of inertia of a body is its ability to resist angular acceleration. It determines the amount of torque that a body needs for a desired angular acceleration about a rotational axis. The moment of inertia of a body is given by the sum of the moments of inertia of each particle, and for each particle the moment of inertia is the product of the mass and square of the distance of the particle from the rotational axis.
Therefore we can write the moment of inertia as,
Now mass has a unit of length. So we can write the dimension of mass as,
The radius of gyration is the unit length. So we can write the radius as,
So the moment of inertia has a dimension of,
We can write this as,
So the dimension of moment of inertia can be calculated as
The moment of inertia is the rotational equivalent of mass in the translational motion.
Now since mass is a scalar quantity, so the moment of inertia is also a scalar quantity.
Note
The dimensional formula is an equation which gives the relation between the fundamental units and the derived units in the terms of dimensions. In mechanics we take the length, mass and time as the three fundamental dimensions and they are represented by
Recently Updated Pages
Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 Maths: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Trending doubts
Which one is a true fish A Jellyfish B Starfish C Dogfish class 11 biology CBSE

The flightless birds Rhea Kiwi and Emu respectively class 11 biology CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

1 Quintal is equal to a 110 kg b 10 kg c 100kg d 1000 class 11 physics CBSE
