2.1

balancing seesaw

-a balance seesaw experiences no overall gravitational torque about its pivot, if nothing twists i the balanced seesaw is inertial, net torque on it is zero. when 2 kids sit on opposite ends each child's weigh produces a gravitational torque on the seesaw about it's pibot, but those two toruqes have opposite directions and thus at lease partially cancel. if the 2 kids have equal weights and are sitting equal distances from the pivot, the two gravitational torques cancel out and sum to 0. The seesaw then experiences no overall gravitational torque about its pivot and balances.

ex a merry go round is already challening to spin empty, and even harder to start or stop when there are lots of children on it. Why is it so hard to change a full merry go round's angular velocity

-a full one has huge rotational mass, and starting or stopping it involves angular acceleration. You exert a torque, and it undergoes angular acceleration, and this depends on rotational mass, which in turn depends on how much mass it has and how far that mass is from the axis of rotation.

angular position

-a physical quantity associated with rotational inertia -describes the seesaw's orientation relative to some reference orientation, it can be specified by determining how far the seesaw has rotated away from its reference orientation and the axis or line about which that rotation occurred. -VECTOR quantity. pointing along the rotation axis with a magnitude equal to the rotation angle. -SI unit of angular position is the radian

angular acceleration

-for you to undergo angular acceleration you must experience a toruq. -VECTOR QUANTITY or rotational motion. Magnitude and direction -measures rate at which angular velocity is changing with time. -SI unit radian per second ^2. -angular acceleration=net torque/rotational mass -same direction as the net torque exerted on it *** decrease in rotational mass, must be accompanied by a corresponding increase in angular acceleration. ex a doll house's seesaw's rotational mass will decrease and the angular velocity will increase compared to the playgrounds, even with identical net torques.

Lever arm

-the longer the lever arm, the less the less force it takes to cause a particular angular acceleration. ***you you obtain more torque by exerting that force father from the pivot or axis of rotation -the shortest distance and direction from the pivot to the place where you push on the seesaw is a vector quantity, a lever arm. -when you push on the seesaw exactly where the picot pass through it, nothing happens, as you keep moving away from it the less harder you have to push, or when you push its end directly toward or away from the pivot, when the force is directed parallel to the lever arm, as it is in this case, it produces no torque on the seesaw -torque is proportional to the length of the lever arm. --producing a torque with a force is that your force must have a compnent that is perpendicular to the lever arm and only that perpendicular component contributes to the torque. -TORQUE = LEVER ARM times FORCE PERPENDICULAR TO LEVER ARM. -the direciton of the force and lever arm also determine the direction of the torque. Right hand rule: if you point your right index finger in the direction of the lever arm and your bent middle finger in the firection of the force, then your thumb will point in the direction of the torque.

angular velocity

-vector quantity of rotational motion. Measures the rate at which the seesaw' angular position is changing with time. -Its magnitude is the seesaw's angular speed -SI unit is radian per second

center of rotation

-when examining rotational motion, the point around which all the physical quantities of rotation are defined. -for a free object, the natural pivot point is its center of mass, for something like like a door example pivots about its hinges.

causing the angular acceleration in a seesaw

1. a boy can push on the ground with his feet so that the ground pushes back and thereby produces an additional torque on the seesaw. Although the seesaw remains balanced, the extra torque from the ground causes it to undergo angular acceleration. When the boy stops pushing on the ground, the ground's torque vanishes and the seesaw resumes a constant angular velocity. 2. they can change their lever arms and thereby unbalance the seesaw. If on girl leans closer the the pivot, that girl's lever arm decrease and so does her gravitational toruq. Since the kids gravitational torques no longer sum to zero, the seesaw isn't balance--it experiences and overall torque due to gravity--and undergoes angular accleration.

ex trying to remove rusty screws using a wrenth with a .2 meter handle. even when you push as hard as you can on the handle, you can't produce enough torque to loosen one of the screws. You have a 1.0 meter pipe that you can slip over the handle of the wrench the make the wrench effectively 1 meter long. How much torque will you then be able to exert on the screw?

5 times as much torque as before. the pipe increases the wrench's lever arm by a factor of 5, from .2 to 1.0 meter. the same force exerted five times as far from the pivot with produce five times as much torque about that pivot. Extending the handle of a lever like took is common technique to increase the available torque

EX a rubber basketball floats in a swimming poo. It experiences zero torque. If you spin the ball and then let go, how will it move?

It wil continue to spin at a steady pace about a fixed rotational axis. Because the ball is free of torques, the outside influences that affect rotational motion it has a constant angular velocity.

EX loading a large container ship requires care in balancing the cargo and fastening it down firmly. the effective pivot about which the ship can rotate in the water is located along the center line. why is improperly loaded cargo dangerous?

a substantial shift in the cargo's position during a storm can unbalance the ship, giving rise to gravitational torque that may cause the ship to rotate about the effective pivot and could capsize.

Newton's 3rd law of Rotational motion

for every torque that one object exerts on a second object, there is an equal but oppositely directed torque that the second object exerts on the first object -applies only to pairs of forces or torques that two objects exert on one another. In such cases only, the forces or torques must be equal but oppositely directed. Two forces or torques exerted on the same object are never a Newtons 3rd law pair and can have any values, including equal but not oppositely direction EX: you stand on the slippery ice and reach up overhead to unscrew a light, as you twist the light you begin to rotate because the light exerted a torque on you. To unscrew the light you must exert a torque on it. In accordance with the law, that light exerts an equal but opposite torque on you. The ice is too slippery to exert a torque on you, so you undergo angular acceleration and

seesaw

for simplicity if you ignore the mass and weight of the seesaw itself, there are then only three forces acting on the occupied seesaw, two downward forces (the weights of the 2 children) and one upward force (the support force of the central pivot) -because the seesaw's fixed pivot always provides just enough upward and sideways force to keep the seesaw from accelerating as a whole, the seesaw always experiences zero net force and never leaves the ground.

Center of Mass

how you distinguish and objects translational motion from its rotational motion. -special point in or near a free object about which all of its mass is evenly distributed and about which it naturally spins. The axis of rotation passes right through this point, so that as the free object rotates, the center of mass doesn't move unless the object has an overall translational velocity. Ex: as a juggler's club arcs through space, its center of mass follows the simple path, and at the same the club's rotational motion about its center of mass is that of an object that's free of outside torques, if its not wobbling it rotates with constant angular velocity.

rotational inertiaq

if the seesaw is stationary, it will remain stationary, however if its rotating it will continue rotating at a steady pace about a fixed line in space. -A body that's rotating tend to remain rotating a body thats not rotating tends to remain not rotating. -physical (vector) quantities associated with rotational motion: orientation(angular position) and angular velocity

angular speed

magnitude, the angle through which the seesaw turns in a certain amount of time and its direction is the axis about which that rotation proceeds -angular speed=change in angle/ time.

Rotational motion

motion around a fixed point (which prevents translation) -seesaw can turn about its pivot thus it experiences this kind of motion -the whole point of a seesaw is that it can rotate so that one cild rises and the other descends. (you may not think of this as rotating, but think of if the ground were not there) -the seesaw starts out not rotating at all. when we release the seesaw it begins to rotate clockwise. The seesaw's rate of motion increases continuously in the clockwise direction until the seesaw strikes the ground. -vector quantities: angular acceleration, torque, and angular position

torque

outside influence, technical term for twists and spins. Ex. When you twist off the lid of a jar your'e exerting torque. --Second important vector of rotational motion -a magnitude and direction, the more torque you exert on a seesaw the more rapidly its angular velocity changes. -direction of the angular velocity is the same as the torque -SI unit is N times m.

translational motion

overall movement of an object from one place to another.

Mechanical advantage

seesaw viewed as a lever that provides mechanical advantage necessary for a light child sitting far from pivot to do work of lifting a heavy child sitting near pivot -each child pushes down on the board with a force equal to that kid's weight, the force directed perpendicular to the lever arm from the pivot to the force, so it produces a torque on the board about the pivot. If the children are properly situated on opposite sides of the board, their torques cancel and the seesaw experience zero net force. -when it roates, thedecending child does work on the board by pushing it down as it move down, and the board does work on the rising child by pishing that child up as the child moves up. Because the seesaw is balanced, the work done on the board by the descending child is equal to the work done by the board on the rising child--> board transfer energy perfectly from the descending child to the rising one ***-because a child travels must father than the adult, the child's work on the seesaw equals the seesaw's work on the adult.: a small force exerted for a long distance on one part of a rotating system producing a large force exerted for a short distance else in that system. -balanced seesaw: each child is using the board to exert a torque on the other child about the pivot, and that torque cancels the other child's gravitational torque.

Newton's 1st Law of Rotational Motion

states that a rigid object that is not wobbling and is not subject to any outside influences (torques) rotates at a constant angular velocity, turning equal amounts in equal times about a fixed axis of rotation. -excludes object that wobble or can change shape as they rotate.

net torque

sum of all individual torques being exerted on it -ex: if a seesaw is experiencing several torques at once, it can't respond to them individually, instead it undergoes angular acceleration in response to the net torque it experience. -net torque=rotational mass times angular acceleration

EX when you cut cardboard with a pair of scissors, its best to move the cardboard as close as possible to the scissor's pivot because...

the closer the cardboard is to the pivot, the more force it must exert on the scissors to produce enough torque to keep the scissors from rotating closed. When the cardboard is unable to produce enough torque, the scissors cut through it. When you place paper close to the pivot of a pair of scissors, you are requiring that paper to exert enormous forces on the scissors to keep them from rotating closes. Rotations are started and stoped by torques and forces exerted close to the pivot exert relatively small torques.

center of gravity

the effective location of the seesaw's overall eight is located at the pivot. With two children riding it, the balance seesaw has a considerable weight, yet that weight produces no torque on the seesaw about its pivot. -although gravity gives the children and the board their own individual weights, there is a unique point, the seesaw's center of gravity-about which all those individual weights are balanced and which gravity effectively pulls down on the entire seesaw. With the seesaw' center of gravity located at the pivot, gravity has no lever arm with which to produce a torque on the seesaw about the pivot.

axis of rotation

the line in space about which the seesaw is rotating.

rotational mass

the measure of an object's rotational inertia, its resistance to changes in its angular velocity. Depends both on its ordinary mass and on how that mass is distributed within the object -The SI unit is kg times m^2. Because the seesaw has rotational mass, its angular velocity will change only if something twists it or spins it, it must experience torque. -the larger the rotational mass, the more slowly its angular velocity changes in response to a specific torque. Ex spinning a basket ball with your finger versus a bowling ball. -also depends on an object's shape., particularly on how far each portion of its ordinary mass is from the axis of rotation. The farther a portion of mass is from that axis, the more rapidly it must accelerate as the entire object undergoes angular accelerate, and the more leverage it has to with which to oppose that acceleration. ***an object that has most f its mass located near the axis of rotation will have a much smaller rotational mass than an object of the same mass that has most of its mass located far from that axis. Ex: a ball of pizza dough has a smaller rotational mass than the finished pizza, the bigger the pizza gets the harder it is to start or stop spinning.

EX. a claw to remove nail on back of hammer, when you slide the claw under the nail's head and rotate the hammer by pulling on its handle, the claw pulls the nail out of the wood. The hammer's head contacts the wood to form a pivot thats about 10 times closer to the nail than to the handle. The torque you exert on the hammer twists it in one direction, while the torque that nail exerts on the hammer twists it in the opposite direction. The hammer isn't undergoing any significant angular acceleration, so the torques must nearly balance. If you're exerting a force of 100N on the hammer's handle, how much force is the nail exerting on the hammer's claw?

the nail is exerting about 1000N since the nail is 10 times closer to the pivot, the nail must exert 10 times the force on the hammer to create the same magnitude of torque as you do pulling on the handle. As the nail pulls on the hammer the hammer pulls on the nail. Although the wood exerts frictional forces on the nail to keep it from moving, the extracting force overwhelms this friction and the nail slides slowly out of the wood.

Newton's 2nd law of rotational motion

the net torque exerted on a rigid object that is not wobbling is equal to that object's rotational mass ties its angular acceleration. The angular acceleration points in the same direction as the net torque. ****any change in net torque you exert must be accompanied by a proportional change in its angular acceleration. Ex: harder you twist, more rapidly its angular velocity change.

Right Hand Rule

to resolve whether it is rotating clockwise or counterclock wise. -We choose to view the seesaw from the direction in which it appears to be rotating clockwise and say that the seesaw' rotation axis points away from out eye toward the seesaw. -call right hand rule because if the fingers of your right hand are curling around the axis in the way the see saw is rotating then you thumb is pointing along the seesaw' rotation axis.

EX when a fiver does a rigid, open somersault off a high diving board, this motion appears quite complicated. Can this motion be descibed?

yes, his center of mass falls smoothly, obeying the rules governing falling objects. As he falls, he body rotates at constant angular velocity about his center of mass. His motion can be seperated into translational motion of his center of mass (it falls) and rotational motion about his center of mass (he roates about it at constant angular velocity.)