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6 -- Part 2: .8 Power

- The dancers' bodies are not moving with respect to each other in the photo.
- They are acting like a single object.
- The model of an object that is point-like is not useful in analyzing the balance of dancers.

- There are 231 parts of the object that don't move with respect to each other.

- The place where the force exerts is important.

- A rigid body is a model of an object.

- Buildings, bridges, streetlights, and utility poles are examples of everyday objects that can be modeled as rigid bodies.

- What conditions are needed for a rigid body to remain at rest is the subject of this chapter.

- There are some simple experiments to start with.

- The cardboard is placed on a small surface like a pencil.

- The pencil falls off.
- Since point-like objects don't tilt, the model of the object can't explain it.
- Maybe we should model the cardboard as a rigid body.

- The cardboard tips can be supported on the bottom.

- Pushing a board so it doesn't turn.

- As it moved, we exert the force.

- We push against the cardboard when it moves.

- As it moves, the heart does not turn as turn.

- We had to push through all of the lines to get the cardboard to where we wanted it.

- The cardboard will turn as it moves if it is pushed at the same locations in other directions.

- The object will not turn if a force is put on it directly or away from that point.
- The center of mass appears to be at the geometric center of the board, which is at the center of the object.

- If the idea is correct, we push the lines along which the forces are on the cardboard so that in each experiment all cross at one point.

- Without turning, a cardboard heart is moving.

- The location of the Rolin Graphics object's center of mass is affected by the mass distribution of an object.

- The mass of the object is not evenly distributed around the center of mass, even though the location of the center of mass depends on the mass distribution of the object.
- We will learn more about the prop erties of the center of mass, but we want to caution you not to call it that.

- We couldn't balance cardboard's center of mass at the beginning of the chapter.

- Imagine drawing the center of mass forces on a piece of paper.
- There are two objects that the cardboard interacts with.
- The force of the eraser on the card board is upward.
- Earth exerts a downward force on the cardboard.

- We should go back to the heart-shaped cardboard from the Observational Experi ment Table 7.1.

- The force of the eraser moves through the center of mass.

- All of the object's mass is located at its center of mass when we model it as a point-like object.
- If we apply the rules to the centers of mass, we can apply what we know about point-like objects to rigid bodies.

- You have a framed painting.

- The turning effect of an individual force depends on where and in which direction the force is exerted.
- The inertia of the object's center of mass is not affected by where the force is exerted.

- The turning ability of a force that exerts on a rigid body is covered in this section.

- In the case of a spinning top, the axis may be a fixed physical one, like the hinge of a door.
- In this chapter, we will look at the conditions under which objects that could potentially rotate do not.

- Consider a door.

- The harder you push near the knob, the faster the door starts moving.

- The turning ability of a force is affected by three factors: the place where the force is exerted, the magnitude of the force, and the direction in which the force is exerted.
- Let's make a titative expression for this ability.

- To build a physical quantity that characterizes the turning ability of a force, we need to perform experiments where we exert measured forces at measured positions on a rigid body.

- A meter stick is balanced on a spring scale.

- The scales can be placed and pulled so that the stick does not move.

- The stick does not rotation.

- The Stick does not move because of equal forces pulling at different distances.

- The stick does not move.

- The stick does not move.

- The stick does not move.

- The stick does not move.

- The object is in static equilibrium because the turning ability of the force on the left cancels the turning ability of the force on the right.

- An object does not accelerate translationally if the sum of the forces on it is zero.
- If it is original y at rest and does not accelerate translation, then it stays at rest.

- When the sum of the forces on the cardboard was zero, it could start turning.

- This idea is helped by another simple experiment.

- The forces of Earth and the table on the book do not cause turning because they pass through the book's Y on B1 center of mass.

- The corners of the book cause it to turn.
- The forces are at the same distance from the center of mass.
- You can imagine that the desk has an axis of rotation that goes through the center of mass.
- You would think that the turning effect caused by each force around the imaginary axis is the same as it was for scales 1 and 3 in the experiment.

- T on B rotation is positive.

- The force is exerted from the axis of rotation.

- The force tends to turn the object clockwise.

- The object does not move.

- Let's see if the new quan tity is useful for explaining other situations.
- You can do this experiment at home.
- Lifting a bag with one hand is easy if you hold it at the end.
- When the stick is tilted up, try to hold the handle end of the horizontal.

- The broomstick can turn around an axis through the hand that is closest to you.
- The broomstick is far from the axis of rotation when the bag exerts force.
- In order to determine the turning ability of the bag on the broomstick, we must find a large quantity.
- The bag must be balanced.

- It is difficult to exert force on your hand.

- It's difficult to hold the broomstick to your body.

- The actual direction of the force is not taken into account.
- The turning ability of the force is affected by the angle at which we exert a force relative to the broomstick.

- We know from experience that pushing on a door on its outside edge does not cause it to move.

- The broomstick is being tilted.
- It's easier to hold if we improve our model for the physical quantity.

- There is a constant force of 10.0 N downward at a 90 angle on the far right end of the meter stick.
- On the far left end of the stick, scale 1 will pull at different angles so that the meter stick stays horizontal.
- The turning ability of the force on the right is balanced by the force on the left in all cases.

- Bag on Stick is needed to produce the same turning ability.

- An experiment to determine the angle dependence of the turning ability the turning ability of a force is caused by a force.

- 1u2 is a function of the angle.

- Take a look at the last row of Table 7.3.

- The force makes the angle smaller.

- The sin 30 is 0.50.

- A method to determine the +112.6 N210.5 m21sin 532 is provided.

- The method for calculating the turning ability is shown in Figure 7.10 If the force has a counterclock, the Torque is positive, the Draw the force wise turning ability is negative, and the beam is positive.

- The British system unit islb # ft, while the SI unit is newton # meter, N # m.

- The units of 1N # m2 are the same as the units of energy 1N # m. Torque and energy are not the same.
- The unit of energy and the unit of Torque will always be referred to as joule and newton # meter 1N # m2 respectively.

- An expression for the distance from the axis of rotation to the place where the force is exerted.

- The force makes a 30 angle relative to a line from first and the smal est magnitude Torque last, if you rank the magnitudes of the Torques that the strings exert on the beam.
- If the pivot point is the place where the string exerts the Torques have equal magnitudes.
- The force on the beam needs to be answered.
- Before looking at the answer below, String 5 exerts a force paral el to the question.

- The rank order is t2 + t4 + t1 + t3 + t5.

- The Torque produced by each force is shown to be low.

- Each string tends to turn the beam counterclockwise.

- Pretend that a pencil is the rigid body to determine the sign of the force that exerts on it.

- A method for determining the sign of a Torque.

- A painter stands on a ladder and chooses the axis of rotation where the feet are relative to the ground.
- He is standing with his feet on the ground.
- The Torque was produced by the ladder.

- Our system is not the same as the ladder that Earth exerts on the painter.

- The painter tends to rotate the ladder clockwise about the axis of ro about two different axes of rotation.

- A 37 angle axis is relative to a line from the axis of rotation to the place parallel to the top of the ladder.

- The painter's feet exert a lot of Torque on the ladder.
- The painter's feet exert themselves on the ladder.
- The diagrams show the different axes of rotation.

- When we choose the axis of rotation at the top of the lad der, the downward force by the painter's feet on the ladder tends to rotate the ladder counterclockwise about the axis.
- A line from the axis of College Physics has an angle of 143 with respect to the place where the force is exerted.

- The axis of rotation affects the to Pearson rque.

- We use it.

- The floor tends to exert force.

- An example of a situation in which a force is zero with respect to one axis of rotation but not zero with respect to another is given.

- We can combine our previous knowledge of forces with our new knowledge of Torque to determine what conditions rigid bodies remain in at rest.

- An object can be at rest for a short time.
- A ball that stops for an instant at the top of its flight does not stay at rest.
- The words "with respect to an observer in an inertial reference frame" are an important part of the definition of static equilibrium.
- If an observer is not in a reference frame, an object can accelerate with respect to the observer even if the sum of the forces on it is zero.

- Earth is the most common point of view for observing real-life situ ations.

- The meter stick from spring scale 2 is again suspended.

- The center of mass of the meter stick is no longer the suspension point.
- You and your friend pul on the stick at scales 2 and 3, but not at scales 1 and 3.

- The stick to rotate is caused by pul ing at other positions while pulling at the same posi tions.

A meter stick is equal to 1-6.0 N2 + 9.0 N + 1-1.0 N2 + 1-2.0 N2

- The distances in the equations for each force are determined by this choice.

- A meter stick is shown at the locations shown.

- The sum of the Torques on the meter stick is zero.

- The first pattern is familiar to us.
- You can't zero translational acceleration.
- There is no vertical acceleration because the sum of the vertical forces determine the Torque produced on the meter stick is zero.
- The meter stick couldn't accelerate horizontally because we didn't specify the zontal forces.
- In the experiments presented in the table, the object relative to the axis of net Torque is zero and the meter stick does not start turning.
- In rotation, we will learn.

- If the ob rigid body is at rest with respect to the different parts of the in turning or rotating static equilibrium, the Earth can be combined into server.

- The ends of a standard meter stick can be placed on scales.
- The mass of the meter stick is deduced from the fact that the scales read 0.50 N.

- If you place a brick 40 cm to the right of the left scale, the scale will read it.

- The meter stick is modeled as a scale 1 and scale 2 with a uniform mass distribution.

- Colle ends the stick.

- The place where the scale touches the stick is where we chose the axis of rotation.

Analyzing the situation with the axis of ing the Torque produced by the normal force exerted pc 3/26/12 18p0 x 10p5 rotation on the left side of the meter stick by the left scale on the stick zero

- It sounds reasonable that the condi is positioned closer to it.

- The outcome on the meter stick should be zero, as should the sum of the predictions.

- The brick on the stick has a rotation axis that we can choose from, so we have the freedom to do what we want.
- Let's try it again with the axis of rotation at ity around the axis of rotation and produce a negative 40 cm from the left side of the brick.
- See the numbers.
- The stick force diagram shows the force exerted by the right scale.
- The force condition of equilibrium has a counterclockwise turning ability and does not depend on the choice of positive Torque.
- The stick has zero Torque since it is at the axis of rotation.

- The axis of rotation has moved to a new position.

- The stick has to exert a balancing force on the brick.

- When we chose a Rolin Graphics xis of rotation at the left end, it was new.

- The left scale on the stick exerts 0 force on LS.

- Earth and the brick exert force on the meter stick.

- The force on the left end is greater because of the brick's choice of the axis of rotation.

- Chapter 7 extended bodies at rest of rotation does not affect the results.
- The meter stick tips over the edge if it is extended more than 30 cm.

- Stick doesn't affect the outcome of an experiment.
- The outcome of actual experiments should not be affected by the concepts of axes of rotation and coordinate systems.

- A uniform meter stick with a 50-g ob ject is positioned as shown below.
- The edge of the table has a stick over it.
- If you push the stick to the side, it tips over.
- The mass of the meter stick can be determined using this result.

- It is helpful to place the axis on the rigid body where the force you know least about is exerted.
- You can use that equation to solve for some other unknown quantity when the force drops out of the second equilibrium condition.

- The human body is a good example of an extended body not being rigid.

- The rest of the body is at a lower elevation so that her center of mass is always slightly below the bar.

- We change the position of our center of mass with respect to other parts of the body a lot.
- Try this experiment.
- Try to stand up without using your hands.
- If your back is vertical, you can't raise yourself from the chair.

- The front of the abdomen is the center of mass for an average person.
- If you managed to lift yourself off the chair and keep the back straight, the experiment would look like a force diagram.

- Earth and the floor exert downward and upward force on your feet.
- The rotation of the chair is caused by the Torques caused by these two forces.

- To stand, you have to tilt your head in a clockwise direction and move your feet under the chair.

- You don't have to use your hands to get out of a chair.

- You should bend forward so that your feet are on the floor.

- Torques caused by these two forces allow you to stand without touching the chair seat.

- Section 7.1 deals with the location of an object's center of mass and how to push it on a smooth surface.
- At dif ferent locations on the object, we found that lines drawn along the directions of the pushing forces all intersect at the center of mass.
- It is impractical to find the center of mass in a diffi cult.
- The method of balancing the object on a pointed support was investigated.
- This isn't very practical with respect to humans.

- Blocks are represented as an expression for the center of mass.

- The system exerts 1 forces.

- The total of al Torques ex- the force of gravity on the system is zero.

- Each of the people blocks are modeled as point-like objects and the seesaw is modeled as a rigid or body.
- To get an expression for the location of the center of the force.

- Let's look at this result.

- If the result makes of all forces relative to sense, then we know the locations.
- There are no people sitting on the ground.

- We assumed its mass was uniformly distributed.
- If we increase the mass of one of the people on the seesaw, the location of the center of mass moves closer to them.

- The term "center of mass" is not true.
- The weight lifter is on each side.
- This is not the case.

- 30 kilo is the number 3.

- The origin can be anywhere.
- The center of mass of per son is on the left side.

- The mass on each side of the center of mass is not equal.

- There is more mass on the left side of the center of mass than on the right side.

- There will be 3 m of balance here.

- There is more mass on the left side of the center of mass than on the right side.

- The whole system of seesaw will balance here.

- The mass of people are not equal.
- The mass on the left side of the center of mass is more than the mass on the right side.
- The larger mass on the left is closer to the center of mass than the smaller mass on the right.
- Torques of equal magnitude are caused by the product of mass and distance on each side.
- We could change the center of mass to be the center of Torque, but since this is not the term used in physics, we still use the term center of mass.

- The mass on the left and right side of the center of mass may not be equal.

- The two fingers are shown below.
- 2 are connected by a rod.
- How does the mass of the knife on the left compare to the mass of the knife on the right?

- The mass of the handle end must be greater than the mass of the bread knife.

- A barbel has a 10- kilo plate on one end and a 5- kilo plate on the other.
- The center of ward normal force and Earth exerts a down mass of the barbell, which is also the balance point for ward gravitational force.
- The plates on the ends must be connected by two forces if the rod is to be stable.

- There is 0.67 m from the end.

- It would tip.
- The New Rolin Graphics force is at the knife's center of mass.
- The 13p0 x 6p7 center of mass must be above the finger.

- Earth on each side of the center of mass has the same magnitudes, but the objects themselves are not necessarily equal.

- In front of the elbow joint, the muscles in the upper arm pull up on your forearm.
- Push down on the forearm.

- The Biceps equilibrium equations allow you to estimate the muscle tension forces.

- The general strategies are applied on the right side of the table.

ceps contracts to push down

- Imagine holding a 6.0- kilo lead ball with your arm bent.
- The elbow joint is 0.35 m from the ball.
- The bicep muscle is attached to the forearm 0.050 m from the elbow joint, and it exerts a force on the forearm that allows it to support the ball.
- The elbow joint is 0.16 m from the center of the 12-N forearm.
- The bicep muscle exerts force on the forearm and the upper arm exerts force on the forearm at the elbow.

- The axis of rotation is where the upper arm bone is.
- The forearm is pressed at the elbow joint.
- The axis of rotation will be eliminated.

- Pick a system for analysis.

- The system of interest is the forearm and hand.

- Decide if you will model the sys as a rigid body or a point-like object.

- The coordinate and hand should be included.

- The force diagram can be used to apply the equilibrium con t.

- If you want to find interest, solve the equations for the quantities of Substitute sin 90 and rearrange the equation.

- Biceps' magnitudes are reasonable and if they are 3112 N210.16 m2 + 159 N210.35 m 24 > 10.050 m2 they have the correct signs and units.

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