Name: _______________________________________ Date: _________________ Hour: _____________

Honors Physics Chapter 11 Note Packet : Rotational Mechanics

11.1 Torque- Every time you open a door, turn on a water faucet, or tighten a nut with a

wrench, you exert force. This turning force produces a _______________.- Torque is different from force. - If you want to make an object move, apply a _______________.- Forces tend to make things accelerate. - If you want to make an object turn or rotate, apply a _______________.- Torques produce _______________.

- A torque is produced when a force is applied with “_______________”. - When the force is perpendicular, the distance from the turning axis to the

point of contact is called the lever arm.- If the force is not at a right angle to the lever arm, then only the

perpendicular component of the force, F⊥, will contribute to the torque.

Torque is defined as: torque =

- So the same torque can be produced by a large force with a short lever arm, or a small force with a long lever arm. Greater torques are produced when both the _______________ and _______________ are large.

- Although the magnitudes of the applied forces are the same in each case, the torques are different. Only the component of forces _______________ to the lever arm contributes to torque.

- Explain why this is a common misconception: Torque and force are the same concept.__________________________________________________________________________________

Watch Out!- We say torque = Fd, and in the previous chapter we said work = fd. The distance for torque is not the

same as the distance used for work.- In work, the distance d is the distance the “force moves” (parallel to the force). In torque the distance d

refers to the leverage distance (perpendicular to the force). The ratios d/d for levers and seesaws, however, turn out to be the same.

Questions1. If a doorknob were placed in the center of a door rather than the edge, how much more force would be

needed to produce the same torque for opening the door?__________________________________________________________________________________

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2. If you cannot exert enough torque to turn a stubborn bolt, would more torque be produced if you fastened a length of rope to the wrench handle as shown?

__________________________________________________________________________________

11.2 : Balanced Torques- Children can _______________ a seesaw even when their weights

are not equal. - Weight alone does not produce rotation _______________ does.- Children soon learn that the distance they sit from the pivot point is

as important as their weight. The heavier boy sits shorter distance from the fulcrum (turning axis) while the lighter girl sits farther away.

- Balance is achieved if the torque that tends to produce _______________ rotation by the girl.

Do the Math1. What is the weight of the block hung at the 10 cm mark?

11.3 Torque and Center of gravity- A force must be applied to the _______________ of an object for it to spin.

a. If the football in line with its center, it will move without ____________.b. If it is kicked above of below its _______________, it will rotate.

11.4 : Rotational Inertia - Inertia: an object at _______________tends to stay at _______________,

and an object in motion tends to remain moving in a straight line. - There is a similar law of rotation: an object rotating about an axis tends to

keep rotating about that axis.- The resistance of an object to changes in its rotational motion is called

____________ ____________. Rotating objects tend to keep rotating while non rotating objects tend to stay nonrotating.

- Just as it takes a force to change the linear state of motion of an object, a torque is required to change the rotational state of motion of an object.

- In the absence of a net torque, a rotating top keeps rotating, while a _______________ top stays _______________.

- Like inertia in the linear sense, rotational inertia depends on mass. - But unlike inertia, rotational inertia depends on the _______________ of the mass.

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- The greater the _______________ between the bulk if the mass if an object and the axis about which rotation takes place, the greater the rotational _______________.

- For similar mass distributions, short legs have less rotational inertia than long legs.

- The rotational object of an object is not necessarily a __________ quantity.- It is greater when the mass within the object is extended from the

_______________ of rotation. - You can try this with your outstretched legs. Swing your outstretched leg back

and forth from the hip. Now do the same thing with your leg bent. In the bent position it swings back and forth more easily. To reduce the rotational inertia of your legs, simply bend them. That’s an important reason for running with your legs bent - bent legs are easier to swing back and forth.

Formulas for Rotational Inertia- When all of the mass m of an object is concentrated at the

same distance r from a rotational axis (pendulum or tire on its center), then the rotational inertia_______________.

- When the mass is more spread out, as in your leg, the rotational inertia is less and the formula is different.

- It is not important for you to learn these values, but you see how they vary with the shape and axis.

- Supposing the shapes in Figure 11.14 all have the same mass and radius (or length), which would be the easiest to start spinning about the axes indicated?

- Which would be the most difficult to start (or stop) spinning?

Rotational Inertia and Rolling- Objects of the same _______________ but different _______________

accelerate equally when rolled down an incline.- A cylinder with small rotational inertia will roll down an incline more quickly

than a cylinder with a greater rotational inertia because it requires more _______________ to start rolling.

- A solid cylinder has _______________ rotational inertia and will roll down an incline more quickly.

- A hollow cylinder has _____________ rotational inertia because its mass is located farthest from the axis of rotation, so it will take longer.

- When swinging your leg from your hip, why is the rotational inertia of the leg less when it is bent?

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- A heavy iron cylinder and a light wooden cylinder, similar in shape, roll down an incline. Which will have more acceleration?

11.5 : Rotational Inertia and Gymnastics- The human body has _______________ principal axes of rotation.

They are all at right angles to the others (mutually perpendicular).

1. Longitudinal Axis - Rotational inertia is _______________ about the longitudinal

axis, which is the vertical head-to-toe axis, because most of the mass is concentrated along this axis.

- A rotation of your body about your longitudinal axis is the _______________ to perform.- Rotational inertia is _______________ by simply extending a leg or the arms.

2. Transverse Axis - You rotate about your transverse

axis when you perform a _______________ or a flip.

3. Rotational axis (front-to-back axis) - Rotational inertia is _______________ when the

axis is through the hands, such as when doing a somersault on the floor or swinging from a horizontal bar with your body fully extended.

11.6 : Angular Momentum- Newton’s first law of _______________ for rotating systems states that an object or system of objects

will maintain its angular momentum unless acted upon by an unbalanced external torque. - Anything that rotates keeps on rotating until something stops it.

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- Angular momentum is defined as the product of rotational inertia and rotational velocity: Angular momentum =

- It is the counterpart of linear momentum: Linear momentum =

-- The lightweight wheels on racing bikes have less angular momentum than those on recreational bikes,

so it takes _______________ _______________ to get them turning.

11.7 : Conservation of Angular Momentum- Angular momentum is conserved for systems in _______________.- The law of _______________ of angular _______________ states that if

no unbalanced external torque acts on a rotating system, the angular momentum of that system is _______________.

- With no external torque, the product of rotational inertia and rotational velocity at one time will be the _______________ as any other time.

-- Rotational _______________ is controlled by variations in the body’s rotational _______________ as

angular momentum is conserved during a forward somersault. This is done by moving some part of the body toward or away from the axis of rotation.

- Although the cat is dropped upside down, it is able to _______________ so it can land on its feet.

Question Time1. The rotational inertia of an object is greater when most of the mass is located..

a. Near the centerb. Off center

c. On the rotational axisd. Away from the rotational axis

2. How many principal axes of rotation are found in the human body?a. One b. Two

c. Threed. Four

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