Chapter 11

Section 11.1 Torque
Torque: happens when you open a door, turn on water faucet, or tighten a nut with a wrench. Torque is different than force. Torque does produce rotation. Torque happens when a force is applied with”leverage". The same amount of torque can be produced by a large force with a short lever arm or a small force with a long lever arm.
Torque=force * lever arm
Lever Arm: The perpendicular distance between an axis and the line of action of a force that tends to produce rotation abou that axis
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Section 11.2 Balanced Torques
Balanced Torques can be two kids on a seesaw. They can balance a seesaw even when the two kids do not weigh the same weight. Where the kids sit on the seesaw depends on how it will balance. The person that is heavier would it a short distance from the fulcrum. But a lighter person would sit farther away.
Balance: the torque that tends to produce clockwise rotation by the boy equals the torque that tends to produce counterclockwise rotation.
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Section 11.3 Torque and Center of Gravity
When you bend down to touch your knees when you’re against a wall you will find that you rotate forward. There is no base below your center of gravity so that will cause you to topple over. When the area beneath your feet is beneath your CG there is a torque. When there is a force on a projectile and it is around the CG then the object will just move around the object as a whole. When the object rotates around it's self there is a torque.
Ex: When you throw a ball there is a force applied to its axis and to the edge of the object.
Section 11.4 Rotational Inertia
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Law of Rotation: An object rotation about an axis tends to keep rotating about the axis.
The resistance of an object to changes in its rotational motion is called rotational inertia. When an object rotates it tends to keep rotating and with non-rotating objects they tend to stay non rotating. A torque must also be present in order to change the rotation of the object. With out torque a rotating top keeps rotating. Rotational inertia depends on the mass of the object. It also depends on the distribution of the mass. The greater the distance between the mass of an object and the axis would depend on the rotation that takes place.
Baseball bat held near its end has more rotational inertia than a short bat.external image cj_GC187_Rawlings_Baseball_bat_free_engraving_included_in_block_font_shown_bridesmaidgifts_.jpg
Long-legged animals such as giraffes, horses and ostriches run slower than hippo’s dachshunds and mice.
Rotational inertia is not a fixed quantity. The rotational inertia is greater when the mass is within the object and then extended from the axis.
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Try It:
Swing your outstretched leg back and forth from the hip. Then do it with your leg bent. When your legs are bent they swing back and forth more easily. When you run you want to bend your legs because it is to hard to run with out your legs bent.
Formulas for Rotational Inertia:
When mass m is concentrated at the same distance r from the axis then the rotational inertia is I=mr2.
Whichever cylinder has the smaller rotational inertia will have a greater acceleration. Inertia can be thought of as "laziness". When your talking about a hallow cylinder and a solid cylinder and trying to decide which has a greater rotation inertia. To determine this you would decide which has the mass concentrated farthest from the axis of rotation. When looking at a hollow cylinder and a solid cylinder which has the greater rotational inertia? The hallow cylinder. The solid cylinder would roll with the greatest acceleration. Another way to say it is that a hollow cylinder has more "laziness per mass" than a solid cylinder. When you have two objects of the same shape but different sizes they roll down an incline at the same acceleration.
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11.5 Rotational Inertia and Gymnastics

A human can rotate freely about three principal axes of rotation.

  • longitudinal axis: vertical from head to toe. Easiest rotation to do. An ice skater uses this rotation when they are going into a spin

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  • median axis: least common axis of rotation this is used when you do a cartwheel

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  • Transverse axis: you use this when you are going into a somersault or a flip.

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Rotational inertia is the most when your arms and legs are extended into a line and it is the least when your arms and legs are tucked.
Increasing rotational inertia can be done by extending a leg or an arm. When both your arms are out it is about threes times more than when your arms are in at your chest. So when you want to go into a spin you need to have your arms out. Your leg must also be extended. By doing both of these things you can vary your spin rate about 6 times. Rotational inertia is the greatest when the axis is through your hands. When a gymnast swinging their rotational inertia is up to 20 times greater than when she is in the somesault. Rotation will transfer from one axis to another axis. Rotational inertia can vary from different body types.

11.6 Angular Momentum

An object that is rotating has an inertia of rotation and moving objects have an inertia of motion.

Linear momentum is the product of the mass and the velocity of an object. Also called momentum this applies tat speeds much less than the speed of light.

Equation: linear momentum = mass X velocity

Angular momentum is the product of rotational inertia and rotational velocity. Angular momentum has a direction and a magnitude.

Equation: angular momentum = rotational inertia X rotational velocity angular momentum = mvr
Rotational velocity the reluctance of an object to change its state of rotation, determined by the distribution of the mass of the object and the location of the axis of roation or revolution.

An object will maintain its angular momentum unless there is an unbalanced. A torque is produced when the center of gravity is not supported.

11.7 Conservation of Angular Momentum

The Law of Conservation of Angular Momentum: if no unbalanced external torque acts on a rotating system, the angular momentum of that system is constant.

When there's no external torque, then the rotational inertia and rotational velocity will be the same. Example: when you stand on a turntable holding weights with your arms extended. Because the weights are extended the rotational inertia is bigger. As you turn the angular momentum is the product of rotational inertia and rotational velocity. When you pull the weights in towards you the rotational inertia is decreased. The result is that the rotational speed increases.

The Law of Momentum Conservation is seen in the movement of planets. It will be a fact of life and people rotating in space habitats who head for far away places.
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