00:01
In this question we are given a t -shaped bar that's free to rotate and subject to a number of forces at different places around its body.
00:12
And we're going to use the sum of the torques from those forces to find the angular acceleration of the bar.
00:20
So the first thing to remember is that we're going to calculate torque as rf sine theta, where theta is the angle between the distance from the axis of rotation and the force.
00:45
So i like to think of this as the component of force that is perpendicular to the distance from the axis of rotation.
00:56
And that's a little different way of thinking about it than a lever arm, which is the perpendicular distance from the axis of rotation to the line of action of the force.
01:10
But this i find to be a little bit conceptually easier.
01:14
Mathematically it's the same.
01:15
If you're in calculus -based physics and you have to use a right -hand rule to get a cross product, you end up with the same direction.
01:22
So, you know, since here we don't actually have to work out a cross product, we're going to go with the slightly easier way.
01:33
Okay, so, like i was saying, we're going to find net torque equals i alpha, so use the sum of the torques, equals the moment of inertia multiplied by this angular acceleration.
01:48
And we're going to remember that forces that produce counterclockwise rotation are positive, and anything producing clockwise rotation is negative.
02:01
So looking around, f1 would have a component that would produce a counterclockwise rotation, f4 is going to have a component that produces a counterclockwise rotation.
02:20
We're just going to write all of this counterclockwise, counterclockwise.
02:24
F3, likewise, is going to produce a counterclockwise rotation, and f2 is our sole clockwise rotation candidate...