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Forces can make objects move, but they can also make objects spin. When this happens, the force exerts a so-called moment on the object, and it is this moment that makes the object spin. Take a moment to learn about moments!In daily usage, the word moment often refers to a short period of time, but in physics, there is a…

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Moment Physics

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Jetzt kostenlos anmeldenForces can make objects move, but they can also make objects spin. When this happens, the force exerts a so-called moment on the object, and it is this moment that makes the object spin. Take a moment to learn about moments!

In daily usage, the word moment often refers to a short period of time, but in physics, there is a very different meaning to the word.

In physics, a **moment** on an object is the turning effect on that object caused by a force.

If there is a nonzero net moment on an object, the object will rotate around a pivot point. On the other hand, if an object is balanced (i.e. not spinning or spinning at a constant rate), then this means that the net moment on the object is zero. This is a situation in which the clockwise moment on an object exactly cancels the anticlockwise moment acting on it.

Suppose we have an object with a clear pivoting point and we put a force$F$on that object. We draw a line through the contact point of the force and in the same direction as that of the force, and we call the perpendicular distance from the pivoting point to that line. See the figure below for an illustration of the setup.

The size of the moment$M$on of the object is then defined as the size of the force$F$multiplied by the perpendicular distance$d$:

$\mathrm{moment}=\mathrm{force}\times \mathrm{perpendicular}\mathrm{distance}$.

Thus, written down using symbols, this equation becomes

$M=Fd$.

This equation for moments is very intuitive. If we exert a larger force on an object, then the moment (i.e. turning effect) increases. If we put the same force on the object but at a larger distance from the pivoting point, then we have more leverage, so the moment increases as well.

From the formula for the size of the moment, we see that the appropriate units of measuring moments are$\mathrm{Nm}$(newton-metres). A force of$1\mathrm{N}$at a perpendicular distance to a pivot of$1\mathrm{m}$exerts a moment size of$1\mathrm{Nm}$. One$\mathrm{Nm}$is the same as one$\mathrm{J}$(joule), which is a unit of energy. Thus, moments have the same units as energy. However, moments are clearly a very different thing than energy, so if we denote a moment, we usually write it down in units of$\mathrm{Nm}$. This particular use of units makes it clear to all readers that we are talking about a moment and not a form of energy.

Let's first look at some qualitative examples of moments.

Suppose your feet were glued to the floor, and someone tries to knock you over. Would they try and push at your ankles or at your shoulders? Assuming you don't want to fall over, you would want him to push at your ankles because this way he can exert only a small moment on you because of the small distance to the pivot point at your feet, and it is not the force but it is the moment he exerts that will make you turn around your pivot (your feet) and fall.

Similar reasoning to the example above leads to the conclusion that people prefer door handles to be on the opposite side of the door that the hinge is, such that the perpendicular distance to the pivot is large and therefore the force required to open the door is small. Let's now take a look at some quantitative examples of calculations with moments.

Let's go back to the figure above. If we push in the indicated direction at a distance of$5\mathrm{m}$from the pivot, then the perpendicular distance will be roughly$4\mathrm{m}$. If we push with a force of$100\mathrm{N}$at this distance in this direction, then we exert a moment of$400\mathrm{Nm}$.

Suppose somebody is stuck in an elevator and you need to break down the door to rescue them. The force at which the door breaks is$4000\mathrm{N}$. This is a lot more than you can exert with your muscles, so you get a crowbar which gives you leverage. If the crowbar is as is depicted in the illustration below, how much force do you need to exert on the crowbar in order to break the door?

Well, we see that we need to exert a moment of$4000\mathrm{N}\times 5\mathrm{cm}=200\mathrm{Nm}$on the door, so the force we need to exert on the crowbar is

$F=\frac{M}{d}=\frac{200\mathrm{Nm}}{1\mathrm{m}}=200\mathrm{N}$.

Suddenly, this force is very realistic for a person to exert on an object, and we are able to break the door.

If you have ever been on a seesaw, then you have unconsciously experimented with moments. Let's examine this familiar situation!

Alice and her dad Bob are sitting on a seesaw and want to make it balance. Alice is lazy and does not want to move, so she stays a distance of$2\mathrm{m}$away from the pivot. The mass of Alice is$20\mathrm{kg}$and the mass of Bob is$80\mathrm{kg}$. At what distance from the pivot does Bob need to sit in order for the seesaw to be balanced?

Answer: For a balanced seesaw, the moments on the seesaw have to cancel each other out, so${M}_{\mathrm{Alice}}={M}_{\mathrm{Bob}}$. The force on the seesaw is perpendicular to the horizontally balanced seesaw, so the perpendicular distance$d$is equal to the distance of the person to the pivot. This means that for a balanced seesaw, we require

${m}_{\mathrm{Alice}}g{d}_{\mathrm{Alice}}={m}_{\mathrm{Bob}}g{d}_{\mathrm{Bob}}$.

The factor of the gravitational field strength cancels out (so this problem has the same answer on other planets too!), and we calculate

${d}_{\mathrm{Bob}}=\frac{{m}_{\mathrm{Alice}}{d}_{\mathrm{Alice}}}{{m}_{\mathrm{Bob}}}=\frac{20\mathrm{kg}\times 2\mathrm{m}}{80\mathrm{kg}}=0.5\mathrm{m}$.

We conclude that Bob needs to sit a distance of$0.5\mathrm{m}$away from the pivot. This makes sense: Alice needs 4 times as much leverage as Bob to compensate for her weight being 4 times as small as Bob's weight.

If you do not know someone's mass, you can figure it out by combining your knowledge of your own mass with observations of your distances to the pivot of a balanced seesaw. Your friend's mass is given by

${m}_{\mathrm{friend}}=\frac{{m}_{\mathrm{you}}{d}_{\mathrm{you}}}{{d}_{\mathrm{friend}}}$.

Let's think about how you would measure the size of a moment. A logical way to go about this is to exert a moment in the other direction and see what moment it takes to cause the object to become balanced or unbalanced. Below is an example to make this process clear.

Suppose you have a spanner and you want to know the size of the moment it takes to undo a certain nut. You get a machine that delivers a constant large force, say$1000\mathrm{N}$, and a string such that you can exert a force on the spanner at a very specific place. See the illustration below for the setup. You then start by placing the string as close to the nut (the middle of which is the pivot) as possible. Chances are the spanner doesn't move, because the distance$d$is so small that the moment on the spanner is also small. Slowly you move the string further and further away from the nut, thereby exerting a larger and larger moment on the nut through an increasing perpendicular distance of the force to the pivot. At some distance$d$to the pivot, the nut starts to turn. You record this distance$d$to be$6\mathrm{cm}$. Then the moment you exerted on the nut was$M=1000\mathrm{N}\times 6\mathrm{cm}=60\mathrm{Nm}$. You conclude that it takes a moment of about$60\mathrm{Nm}$to undo this particular nut.

- A moment on an object is the turning effect on that object caused by a force.
- If an object is balanced, then this means that the net moment on that object is zero. The clockwise moments cancel out the anticlockwise moments.
- We draw a line through the contact point of the force and in the same direction as that of the force, and we call the perpendicular distance from the pivoting point to that line.
- A momentby a forceat a perpendicular distanceis given by.
- We measure the size of moments in.
- Typical practical situations in which moments play a large role are crowbars, seesaws, and spanners.

*M=Fd*, where *F* is the force on the object and *d* is the perpendicular distance of the contact point of the force to the pivot of the object. It is handy to look at pictures to see what we mean by the term perpendicular distance.

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