Angular Momentum: Homework Statement & Equations

[Heat]

Homework Statement

I've uploaded a pic of the problem and my work at the link below:

http://i.imgur.com/K4ukj.jpg"

Homework Equations

I = mR^2 w



Hopefully everything thus far is correct, I'm stuck at finding the rate of change. From what I understood it's essentially the derivative of Angular Momentum with respect to time. Thank you in advance.

 

[Pi-Bond]

The rate of change of angular momentum is torque, or the moment of inertia multiplied by angular acceleration.

 

[Heat]

Thank you Pi-Bond. Does my approach for getting the angular momentum appear to be correct?

 

[Pi-Bond]

Yes, that appears to be correct.

 

[paranormal]

I would like to commend you for showing your work and seeking help when you are stuck. Your understanding of the equations and their application seems to be correct so far. However, as you mentioned, you are stuck at finding the rate of change. This is a common challenge when dealing with angular momentum problems.

In order to find the rate of change of angular momentum, you need to use the equation L = Iω, where L is angular momentum, I is moment of inertia, and ω is angular velocity. In this case, moment of inertia is given by I = mR^2, where m is mass and R is the distance from the axis of rotation.

To find the rate of change, you need to take the derivative of L with respect to time. This will give you dL/dt = d(Iω)/dt = I(dω/dt) + ω(dI/dt). Since moment of inertia is constant in this problem, dI/dt is equal to 0. This leaves you with dL/dt = I(dω/dt).

To find the value of dω/dt, you can use the equation τ = Iα, where τ is torque and α is angular acceleration. In this problem, torque is given by τ = 50N*m and moment of inertia is I = mR^2. Therefore, you can rewrite the equation as 50 = mR^2α. Solving for α, you get α = 50/(mR^2).

Now, you can substitute this value of α into the equation dL/dt = I(dω/dt). This will give you dL/dt = I(50/(mR^2)). Plugging in the values for I and R, you can solve for dL/dt and find the rate of change of angular momentum.

I hope this helps you understand how to approach this problem and find the solution. Remember to always check your units and be careful with your calculations. Good luck with your homework!