# Angular Momentum Dimensional Analysis

• k3r0
So the fact that the dimensions of angular momentum are ML2T-1 tells you that ##L = c m v R## for some constant ##c##, but it can't tell you what ##c## is. It can only give you the correct relationship between the variables.
k3r0

## Homework Statement

"A particle of mass m moves in a circle of radius R. Using dimensional argument,
determine the particle angular momentum."

L = mvr

## The Attempt at a Solution

Because L = mvr, the dimensionality would be ML2T-1. I don't know where to go from here so if someone could point me in the right direction it'd be appreciated.

Thanks!

You need to take the problem backward, compared to what you wrote.

To use a "dimensional argument," you start by the units, and then figure out how to construct an equation (with parameters you know) that will have the correct units.

So start with the fact that the units of angular momentum are ML2T-1, and find a way to argue that this means that ##L = m v R##.

1 person
I should add that dimensional arguments are, at best, correct up to a dimensionless constant.

## 1. What is angular momentum?

Angular momentum is a physical quantity that describes the rotational motion of an object around an axis. It is a vector quantity and is defined as the product of an object's moment of inertia and its angular velocity.

## 2. What is the unit of angular momentum?

The unit of angular momentum is kilogram meters squared per second (kg*m^2/s). It is derived from the units of moment of inertia (kg*m^2) and angular velocity (rad/s).

## 3. How is angular momentum related to dimensional analysis?

Dimensional analysis is a method used to check the validity of equations by comparing the dimensions of the quantities involved. In the case of angular momentum, dimensional analysis can be used to verify the units of the equation L = Iω, where L is angular momentum, I is moment of inertia, and ω is angular velocity.

## 4. Can angular momentum be measured?

Yes, angular momentum can be measured using instruments such as a gyroscope or by analyzing the motion of a rotating object. It can also be calculated using the equation L = Iω, where I and ω can be measured directly.

## 5. How is angular momentum conserved?

According to the law of conservation of angular momentum, the total angular momentum of a system remains constant as long as there is no external torque acting on the system. This means that if the moment of inertia or angular velocity of an object changes, the other quantity will change in the opposite direction in order to keep the total angular momentum constant.

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