Derive an expression that relates angular momentum with the angular velocity of rigid body.
Answers
Answer:
L=mvr
Explanation:
For a rigid body, the angular momentum L is the product of the moment of inertia and the angular velocity:L=Iω. For a point of mass, angular momentum can be expressed as the product of linear momentum and the radius(r):L=mvr.
Question:
Derive an expression that relates angular momentum with the angular velocity of rigid body.
Solution:
See the attachment:
Let's consider a rotating body having n numbers of particles at different radius.
Let their masses be and radii at which they are located be
Now, we know that:
- where L is angular momentum, r is radius, p is linear momentum.
- It can also be written as
- Here, we will take the angle b/w r and p as 90° as we are considering the particle to be perpendicular to the plane it is rotating on. [sin90=1]
Calculating L for each n particle of the rotating body.
For particle m1:
For particle m2
Similarly, for particle mn
Sum total angular momentum:
The relation here we got is :
Angular momentum = Moment of Inertia x Angular velocity.