## Friday, May 12, 2023

Where are we going with this? The information on this page is related to basic astronomy and astrophysics.

Astronomy: A Group-sourced Collection of
Concepts, Information, and Ideas

The following information was compiled by students (group-sourced) as an in-class project.

Refer to the cited sources for additional information.

## Monday, February 27, 2023

### Torque: Types of Levers

Where are we going with this? The information on this page connects to standards such as:

• Gather evidence to defend the claim of Newton's first law of motion by explaining the effect that balanced forces have upon objects that are stationary or are moving at constant velocity.

•Recognize and communicate information about energy efficiency and/or inefficiency of machines used in everyday life.

Torque: Types of Levers
(Hmm… I thought torque was something in car engines!)

Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.

~Archimedes

(As if!)

But, he's not wrong. Mathematically, that is.

Let's dig into this a little!

The concept of levers and torque are directly connected to motion that rotates around a pivot point. This motion can be considered to be clockwise around the point or counterclockwise (anticlockwise).

Every lever system has three parts: the lever, the effort and the load.

And… every lever has two parts.

We are going to call one of those parts the lever arm. The lever arm is the beam or whatever that is used. More on this after we define other parts.

The second part of the lever is a fulcrum. The fulcrum (sometimes called the pivot) is the thing around which the lever arm rotates.

The effort is a force that is applied to the lever arm at some distance from the fulcrum.

The load is also a force that will have an effect on the lever arm

Generally, the effort is acting on the load.

Circling back to lever arm…

The lever arm is the part of a lever system that sits on and rotates around the fulcrum and to which is applied the effort so that it can act on the load.

The effort is trying to rotate the lever arm around the fulcrum. The load is resisting this motion.

It is incorrect to say that if the effort is greater than the load the lever will rotate as desired. Force alone is not enough to determine what will happen.

What determines the rotation is something called torque.

Torque is the potential to rotate the lever and is the product of the applied force and the distance from the fulcrum.

Caveat:
• it is ONLY the vector component of the force that is perpendicular to the lever arm. So, sometimes, you have to deconstruct the force to find the perpendicular component.

Hence, where T is torque, F is force and d is distance from the fulcrum…

T = Fd

Torque adds up in a lever system. Clockwise torque and counterclockwise torque have opposite signs.

If you think of a positive torque as attempting to cause clockwise rotation around the fulcrum, then negative torque will be attempting to cause counterclockwise rotation.

Where T is torque, the net torque will be the signed sum of all the torques acting on the lever, so that…

T(net) = T1 + T2 + T3

If you say that clockwise is positive…

…if the result is positive, then you have clockwise rotation.
…if the result is negative, then you have counterclockwise rotation.

Now, if you want to complicate the math, you can say that the fulcrum is at distance zero, then measure left as positive and right as negative, then say that forces "up" are negative and "down" are positive, then, plug all those in so that…

T(net) = F1d1 + F2d2  + F3d

It will work out…

A more "tangible" approach is to keep up logically with the torques as counterclockwise and clockwise.

Sometimes, you are looking for a solution that results in equilibrium. That is to say that there is either no rotation or that the rotation is occuring at a constant rate.

This would mean that

T(cw) = T(ccw)

In such a case, it's easy and logical to sort the various forces to the appropriate side of the equation.

## Types of Levers

Though there are three types of levers, the math on them is essentially the same:

T(net) = T1 + T2 + T3

The types of levers are categorized according to the configuration of load, effort, and fulcrum.

Class 1 Lever

"For the Class 1 lever the pivot lies between the effort and load. A see saw in a playground is an example of a Class 1 lever where the effort balances the load."

In the above image, if the effort is counterclockwise, then the load is clockwise. So, if the product of effort and distance is greater than the product of load and distance, the lever arm will rotate counterclockwise.

Class 2 Lever

"For the Class 2 lever the load is between the pivot and the effort (like a wheelbarrow). The effort force needed is less than the load force, so there is a mechanical advantage."

In this image, load would be clockwise and effort counterclockwise.  Since torque is distance times force (effort), a small effort would move a larger load.

Class 3 Lever

"For a Class 3 lever the load is further away from the pivot than the effort. There is no mechanical advantage because the effort is greater than the load. However this disadvantage is compensated with a larger movement. This type of lever system also gives us the advantage of a much greater speed of movement."

In this image, load would be clockwise and effort counterclockwise.  Since torque is distance times force (effort), a large effort would be needed to move a smaller load.

___________________________

There can be far more complex arrangements involving multiple efforts and loads. However, the principle remains the same:

Where T is torque, the net torque will be the signed sum of all the torques acting on the lever, so that…

T(net) = T1 + T2 + T3

 Where the roadway is considered the lever arm, each support footing is a fulcrum, each cable is an upward force (effort) and the roadway and every car is a load. It is notable that the upward forces only exist in opposition to the downward forces.