# Determining Torque Lever Arm

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#### m25

##### Full Member
So I've always had problems figuring out what exactly the lever arm is in figuring out a torque problem, in which
Torque=(Force applied)x(Lever Arm)

According to definition I found online, lever arm is "the perpendicular distance from the axis of rotation to the line of action of the force." But this definition does not really makes sense to me. So I tried to figure out what lever arm is in my own method, which I've attached.

So, basically what I did was I draw a straight line through the axis of rotation so it will be parallel to the force(indicated by green line), and the lever arm is the shortest distance between those two parallel lines(indicated by pink line).

So my question is, is this one of the correct ways to determine the lever arm?

#### Attachments

• IMAG1952.jpg
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#### Cawolf

##### PGY-2
7+ Year Member

Torque = r x F = rFsin(theta)

The order is important (not F x r) as it is a cross product, so the direction will be wrong if you write it the other way.

The torque is = rF when the force is perpendicular to the lever arm, and decreases as it moves away from the normal.

Your drawing is correct though - nice work on showing it that way.

If you compare your drawing to the standard formula you will see that the distance d = rsin(theta), so they are the same thing.

#### m25

##### Full Member

Torque = r x F = rFsin(theta)

The order is important (not F x r) as it is a cross product, so the direction will be wrong if you write it the other way.

The torque is = rF when the force is perpendicular to the lever arm, and decreases as it moves away from the normal.

Your drawing is correct though - nice work on showing it that way.

If you compare your drawing to the standard formula you will see that the distance d = rsin(theta), so they are the same thing.

Thanks, so when Torque = rFsin(theta) , theta is just the angle between the force and the lever right? And because my green line going through the axis of rotation is parallel to force vector, then theta is also the angle between the green line and the lever, correct?

7+ Year Member
Yes and yes.