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Torque

A torque() measures the tendency of aforce to rotate an object about some axis(fulcrum or pivot). A twist.

Depends on:

1. the forceapplied2. the length of the lever armconnecting

the axis to the point of force application

3. the anglebetween the two.

http://en.wikipedia.org/wiki/Forcehttp://en.wikipedia.org/wiki/Force

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Examples

A screwdriver turning a screw

A bicycle wheel rotatingThe hands of a clock

A door opening

A merry-go-round rotatingA propeller on a ship

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Application of Torque

The farther the Force is from theaxis, the easier it is to rotate theobject because there is moretorque.

For example, its easier to open a door byapplying force to the edge of the door

than applying the same force closer to thehinge.

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Formula for Torque

= F x dWhere Fis the applied Force and dis the

length of the lever arm

Note: A force of 3N applied 2m from thefulcrum exerts the same torque as 1N

applied 6m from the fulcrum.

the SIunit of torque is the "newtonmeter (Nm).

http://en.wikipedia.org/wiki/SIhttp://en.wikipedia.org/wiki/Newton_meterhttp://en.wikipedia.org/wiki/Newton_meterhttp://en.wikipedia.org/wiki/Newton_meterhttp://en.wikipedia.org/wiki/Newton_meterhttp://en.wikipedia.org/wiki/SI

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Right Hand Rule

The direction of the torque can bedetermined by using the right hand griprule:

curl the fingers of your right hand toindicate the direction of rotation, and stickyour thumb out so it is aligned with theaxis of rotation. Your thumb points in the

direction of the torque vector.

http://en.wikipedia.org/wiki/Right_hand_grip_rulehttp://en.wikipedia.org/wiki/Right_hand_grip_rulehttp://en.wikipedia.org/wiki/Right_hand_grip_rulehttp://en.wikipedia.org/wiki/Right_hand_grip_rule

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Derived Formulas & Net Torque

F = /d

d = /F net= 1 + 2

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Center of Mass The center of massof a system of particles

is a specific point at which the system's massbehaves as if it were concentrated.

It does not always coincide with its intuitive

geometric center. In the case of a rigid body, the position of its

center of mass is fixed in relation to theobject.

Inthe case of a loose distribution of masses

in free space, the position of the center ofmass is a point in space among them.

http://en.wikipedia.org/wiki/Rigid_bodyhttp://en.wikipedia.org/wiki/Free_spacehttp://en.wikipedia.org/wiki/Free_spacehttp://en.wikipedia.org/wiki/Free_spacehttp://en.wikipedia.org/wiki/Rigid_body

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Moment of Inertia A measure of how the mass of an object is

distributed and how easy or hard it is to getthe object rotating (its resistance to changesin rotational motion)

Variable = I Unit = kgm2

A derivation of Newtons 2ndLaw gives us

= I( I is correlated to mass & toforce; a is acceleration)

And I =/ and =/I

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Example:

Find the moment of inertia of barrelrolling down a hill if the torque is 12 Nmand the acceleration is 5.8 m/s2.

I = T/a

I = 12/5.8

I = 2 kgm2

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Moment of Inertia and Torque

The farther the center of mass isfrom the axis of rotation the

greater the moment of inertiaand the harder it is to make theobject rotate.

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Same as Center of Gravity?

In an entirely uniformgravitational field, the center of

mass is often called the centerof gravitythe point wheregravity can be said to act.

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Angular Momentum

Because a rotating object has inertia, italso has momentum associated with itsrotation.

Ex: Isnt it hard to swing a heavy sledgehammer and hard to stop it swinging?

When torque is zero, the angularmomentum of a body is constant and

conserved. The torque ona body determinesthe rate of

change of its angular momentum.

http://en.wikipedia.org/wiki/Angular_momentumhttp://en.wikipedia.org/wiki/Angular_momentumhttp://en.wikipedia.org/wiki/Angular_momentum

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Angular Momentum FormulaL = r x p or L = I x w

L is the angular momentum of theparticle

r is the radius of the circlep is the linear momentum of the particle

(P = Mass X Velocity)I is the moment of inertiaw is angular velocity

Unit is: Nms

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derived formulas

R = L/p

I = L/w

p = L/r w = L/I

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Example:

What is the angular momentum of abicycle wheel with a mass of 20 g and adiameter of 0.50 m. It is rotating at aspeed of 65 mps.

m = 20 g x 1kg/1000g = 0.02 kg p = m(v) = 0.02 kg x 65 = 1.3 kgm/s

r = Diameter/2 = 0.50/2 = 0.25 m

L = r(p) = 0.25(1.3) = 0.325 Nms

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Angular Momentum

The conservation of angular momentumexplains the angular acceleration of an ice

skater as she brings her arms and legs closeto the vertical axis of rotation. By bringing part of the mass of her body

closer to the axis she decreases her body'smoment of inertia. Because angular

momentum is constant in the absence ofexternal torques, the angular velocity(rotational speed) of the skater has toincrease.