I know the angle the moment arm is at, the X and Y components of the force applied to the arm, the location the force is applied at, and can easily determine the angles involved in the situation.
Unfortunately, I'm finding it extremely difficult to find good websites explaining how to calculate the change in the angle of the arm. I'm going to talk it over with my old physics teacher in a couple of days, but I wanted to make sure I have some basic understanding of what's involved before I go in.
Please enlighten me! I appreciate it.
Using torque
Author
So, I've finally started to seriously try and figure out how torque works - I didn't think it would be useful when I was actually in physics :'(.
Sensibly, I'm starting in 2D. Here is a crappy, MS-Paint diagram of the situation:
I know the angle the moment arm is at, the X and Y components of the force applied to the arm, the location the force is applied at, and can easily determine the angles involved in the situation.
Unfortunately, I'm finding it extremely difficult to find good websites explaining how to calculate the change in the angle of the arm. I'm going to talk it over with my old physics teacher in a couple of days, but I wanted to make sure I have some basic understanding of what's involved before I go in.
Please enlighten me! I appreciate it.
I know the angle the moment arm is at, the X and Y components of the force applied to the arm, the location the force is applied at, and can easily determine the angles involved in the situation.
Unfortunately, I'm finding it extremely difficult to find good websites explaining how to calculate the change in the angle of the arm. I'm going to talk it over with my old physics teacher in a couple of days, but I wanted to make sure I have some basic understanding of what's involved before I go in.
Please enlighten me! I appreciate it.
So you're probably aware that the torque τ is a vector quantity defined as the cross product
τ = r x F,
with F the applied force and r the vector from the pivot point to the point where the force is applied.
What you want to calculate is the angular acceleration α, which is found using the following angular version of Newton's second law:
τ = I α.
The quantity I is the "moment of inertia" which depends on both the mass and the geometry of the object. For a rod of length L and mass m it's given by I = 1/3 m L2. Examples for different shaped objects are given here.
Now that you know the angular acceleration, you can work out the change in rotational velocity and the change in angle as usual with the appropriate equations of motion.
τ = r x F,
with F the applied force and r the vector from the pivot point to the point where the force is applied.
What you want to calculate is the angular acceleration α, which is found using the following angular version of Newton's second law:
τ = I α.
The quantity I is the "moment of inertia" which depends on both the mass and the geometry of the object. For a rod of length L and mass m it's given by I = 1/3 m L2. Examples for different shaped objects are given here.
Now that you know the angular acceleration, you can work out the change in rotational velocity and the change in angle as usual with the appropriate equations of motion.
Author
That's pretty helpful - thanks! I'm still not there 100% yet, but I'll be getting that cleared up tomorrow, anyways. Thanks a bunch.
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