How Do You Calculate the Angular Momentum of a Rotating Bat?

In summary, to calculate the angular momentum of a batter swinging a 0.9 m long bat, we need to use the formula L=Iω, where I represents the moment of inertia of the bat. Assuming a mass of 0.6 kg and a rotation of 3 rad/s, we can approximate the bat as a long thin cylinder and find its moment of inertia using the formula I=mr^2. This results in an incorrect answer, as the bat should be assumed to have a uniform density. To find the correct moment of inertia, we can either look it up or derive it ourselves.
  • #1
Exustior
2
0

Homework Statement


A batter swings a 0.9 m long bat. Calculate the angular momentum of the bat relative to its axis of rotation. Assume the bat has a mass of 0.6 kg and rotates at 3 rad / s
(Hint: Approximate the bat by a rod, or a long thin cylinder, and find the moment of inertia.)
Answer in (N m)

Homework Equations


I=mr^2
ω=v/r
v=ωr
L=Iω

The Attempt at a Solution


L=Iω
I=mr^2
so L=(0.6)(.9^2)(ω)
ω=angular velocity is 3 rad/s
so L=(.6)(.9^2)(3rad/s)= Wrong answer
 
Last edited:
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  • #2
Hey, welcome to physicsforums!
uh, the moment of inertia formula you have used is not correct for this problem. The inertia I=(0.6)(0.9)^2 would suggest the mass of the bat is concentrated at the end of the bat. But it looks like they want you to assume the bat is a long thin cylinder, of uniform density. So either you can look up the moment of inertia for this kind of object, or derive it yourself, if you have time.
 
  • #3
BruceW said:
Hey, welcome to physicsforums!
uh, the moment of inertia formula you have used is not correct for this problem. The inertia I=(0.6)(0.9)^2 would suggest the mass of the bat is concentrated at the end of the bat. But it looks like they want you to assume the bat is a long thin cylinder, of uniform density. So either you can look up the moment of inertia for this kind of object, or derive it yourself, if you have time.
Thanks!
I got it I was using the wrong formula.
 

FAQ: How Do You Calculate the Angular Momentum of a Rotating Bat?

1. What is angular momentum?

Angular momentum is a measure of an object's rotational motion. It is the product of an object's moment of inertia and its angular velocity.

2. How do you calculate angular momentum?

To calculate angular momentum, you need to multiply the moment of inertia of the object by its angular velocity. The formula for angular momentum is L = Iω, where L is angular momentum, I is moment of inertia, and ω is angular velocity.

3. What is the unit of angular momentum?

The unit of angular momentum is kilogram-meter squared per second (kg·m^2/s).

4. Can angular momentum be conserved?

Yes, according to the law of conservation of angular momentum, the total angular momentum of a system remains constant in the absence of external torque.

5. How does angular momentum relate to rotational kinetic energy?

Angular momentum and rotational kinetic energy are related by the equation L = Iω = (1/2)Iω^2. This shows that the greater the angular velocity of an object, the greater its angular momentum and rotational kinetic energy.

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