How to find the moment arm ?

Question

Maybe u r not gonna understand the question...
but try,i didn't understand it..
i think it's something dealing with clock wise and anticlock wise!!!

Answer 1

We can write f x L = F X l; where f is a force, F is another force, and L and l are two moment arms. Think of a teeter totter, with a person weighing f on one end and another person weighing F sitting on the other end. The distance f is sitting from the fulcrum of the teeter totter (where the = sign is in the equation) is L. And F is sitting on the other side a distance l from the fulcrum.

As the = in the equation is the fulcrum of the imaginary teeter totter, we see that the f is pushing down on the LHS of the board; so it's pushing the teeter totter in a counter clockwise direction (CCW). That is, for example, if the teeter totter were free to swing around the person at f would start at the 9 o'clock position and swing down to the 6 o'clock position...making time go backwards...CCW.

On the other side (RHS) of the fulcrum, F is pushing down from the 3 o'clock position. F would also end up at the 6 o'clock position, swinging around = which is the pivot point or fulcrum, but this time going in the usual clockwise direction (CW).

Let's see what f X L = F X l means in physics. First of all, it says the LHS equals the RHS when the teeter totter is balanced (the = sign). We can rewrite the equation as F = (L/l)f and note that if L > l this means that F > f to remain balanced (equals). And this is a really useful result.

Why? Because it means I can push down on one end of the teeter totter with a relatively small force f and lift a relatively large F up at the other end. And, ta da, this is called mechnical advantage, which for this example is = L/l > 1.000 So there you have it, the moment arms L and l can be found one way by balancing a board on a fulcrum (e.g., the teeter totter). In which case, we have f X L = F X l so that L = (F/f) l and you can find L the moment arm needed to lift F when F, f, and l are known.

Answer 2

If normal force is +y, that implies the roof is horizontal rather than slanted. Look at the ball and the forces acting on it. The force of gravity is always acting downward (or rather radially toward the center of the earth. If you imagine the ball is divided into many small elements of equal mass, the gravitational force will be about the same on each (there will be a tiny difference, between say an element at the bottom of the ball vs. an element at the top). It shouldn't be too hard to see that instead of a huge number of forces for each tiny element, we can get the equivalent from one force acting on the center of mass of the ball (if the mass is evenly distributed and the ball is a sphere, the center of mass will be at the center of the sphere, even if there isn't any mass at the center, such as with any hollow ball). With this view it should be clear gravity doesn't cause a moment. Furthermore, from experience, if you hold a ball and then just let it fall, it doesn't start spinning, confirming gravity doesn't impart a moment. If you did the experiment for a long distance drop, you'd have to do it in a vacuum to prevent variations in air resistance from causing moments that could turn the ball slightly. The frictional force, however, is acting on the surface of the ball in a direction that is tangential. Thus the force is acting in a direction to produce torque. Consider the simple example of a seesaw that is balanced level. The pivot point is at the center of the seesaw board. In this case, gravity does produce torque. Look at any point on the seesaw: the force of gravity is downward which would tend to rotate the seesaw one way. Because there is another point of mass on the other side of the seesaw experiencing the same magnitude of force which produces a moment in the opposite direction, there's no net torque. For every point on one side, there's a corresponding point the same distance from the pivot on the other side. So we would say the sum of the clockwise moments equals the sum of the counterclockwise moments hence no net moment. Put a rock on one side and you immediately see what happens.

Answer 3

Moment Arm

Answer 4

The moment arm is the distance from the pivot point the force is applied. Using the right-hand-rule any force pointed in the CCW direction is positive and any force pointed in the CW direction is negative. The right hand rule works like this, hold out your right hand with the fingers pointed in the +x direction, curl you fingers towards the +y direction, and your thumb will point in the direction of +z. So, any force that causes a CCW rotation about the z axis is a positive moment, vice versa for a negative. Example, if you have a forces pointed in the +y direction on the +x axis you would hold you hand out towards the force and curl you fingers in the direction it is pointing, which in this case would make your thumb point in the +z direction. If your +y forces was on the -x axis, then to bend your fingers in the correct direction your thumb would now be pointed in the -z direction so the moment created would be negative. Anyways, I hop I could help you out. Good luck.

Answer 5

_____________________________________________--

Suppose a body is rotating about an axis passing through point O when force F is applied at point A on the body.

Let AC represent the line of action of force F

Draw line OA, then OA represents position vector 'r'

From O drop perpendicular OB on AC , the line of action of force

Then, OB, the perpendicular distance of line of action of force from the axis of rotation is called MOMENT ARM

MOMENT ARM is also called LEVER ARM

Using trgnometry,

MOMENT ARM = r sin O

where r is magnitude of position vector 'r' and O is angle between force 'F' and position vector 'r'

The turning effect (torque) of a force is equal to product of magnitude of force and moment arm

torque =t=magnitude of force x moment arm

Torque may be clockwise or anticlockwise

To find direction of torque, use right hand cork screw rule or curl rule
_____________________________________