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Next year show how balanced torque problems can be kept in g and cm more. A Force causes an object to accelerate A Torque causes an object to rotate Torque Force Anytime you rotate an object you apply a torque When you open door, it rotates. Where is the pivot point / axis of rotation? To open a heavy door where would you push on the door to make it easiest? A B C The distance from the pivot point to the location of the force is called the LEVER ARM (distance) A B C The longer the lever arm the greater the torque This force has no lever arm and produces no torque or rotation The direction of the force matters too, how well will these two forces work for opening the door? B A To Rotate an object the force must be applied perpendicular to the lever arm (the door in this case) B A A is perpendicular to the lever TORQUE t=Fd Force perpendicular to lever arm (N) lever arm length (m) NOT distance traveled The greater the torque the faster an object will rotate or turn Where should you hold the wrench in order to loosen a stubborn bolt? t=Fd Torque Force MORE Torque Force A wrench is all about TORQUE You create the most torque by holding the wrench at the end and by exerting a large force. If you can’t loosen the bolt with all your strength, what do you do? Force Force Get a longer wrench!! lever arm Even with the same force, twice the lever arm gives twice the TORQUE The greater the force,the greater the torque t=Fd Torque Force Force MORE Torque The more perpendicular the force the greater the torque t=Fd Torque Force only the blue part counts MORE Torque Force Any force which points through the axis of rotation creates no torque Force t=Fd Torque = 0 What is the torque generated by pushing With a force of 5.0 N on a wrench which is 20 cm long? Torque requirement on your tires lug nuts is 190 Nm. If you have a wrench which is .25 m, how hard do you have to push? .25 m Consider the two wrenches below, compare torques If the applied force is the same F F The lever arm distance is really still the same F F Another way of looking at torque, this is easier in some situtations. 1.) Draw a line through the force 2.) Bring a line perpendicular to the previous line through the axis of rotation 3.) The lever arm is the distance that line to the center of rotation lever arm distance 4.) Torque = Total force x lever arm 1.) Draw a line through the force 2.) The lever arm is the distance that line to the center of rotation 3.) Torque = Total force x lever arm Lever arm distance (d) F 1.) Draw a line through the force 2.) The lever arm is the distance that line to the center of rotation 3.) Torque = Total force x lever arm F Lever arm distance (d) A force of 100 N is exerted as below on a rope attached to a .25 m wrench. What torque is generated? 100 N .2 m F TORQUE is also a vector. We will just think of torque as CW or CCW CCW CW Two 400 N children balance on a seesaw The same force on each side, right 400 N 400 N 1m 1m What if one child scoots in? Forces are still equal on both sides 400 N 400 N 1m 0.5 m BUT THE TORQUES DO NOT 400 N 400 N 1m t = 400 Nm (CCW) 0.5 m t = 200 Nm (CW) Net t = 200 Nm (CCW) To prevent an object from rotating there can be no net TORQUE OR tcw = tccw If there is no net torque then an object does not…. Rotate (its rotation speed does not change is the more accurate statement) If there is no net force then an object does not…. Accelerate Can a big kid and a little kid balance on a seesaw? 100 N 400 N The bigger kid must move closer the to fulcrum to lower his torque 400 N ? 0.25 m 100 N 1m What is the upward force at the pivot point? If the seesaw balances what is the weight of the other person? 400 N .75 m ?N 1m If a 400 N person and a 200 N person want to balance where should be fulcrum be placed? 400 N 200 N d 2d So that the lever arm is twice as much for the 200N person or 2/3 away from them If a 500 N person and a 100 N person want to balance on the ends of a 3 m seesaw where should be fulcrum be placed? 500 N 100 N d 5d So that the lever arm is 5 x as much for the 100N person or 5/6 away from them Correct this statement: An object balances the when weight the same on either weight side is on of theboth pivotsides pointofcreate the pivot equal point torques A mass on a string exerts a torque on a pulley, what is lever arm & direction of torque DEMONSTRATION: Will the object rotate .10 m 500 g .25 m 500 g Torque WS Torque lab Torque Feeler Demo What causes an object to change its rotational speed? How do you create torque? When does a force create NO torque? Which force creates more torque? NEITHER creates any TORQUE, since they both point to the axis of rotation Demo – balanced / unbalanced meterstick is there a net torque? FN = mg Fg = mg Is there a net force? Is there a net torque? FN Fg IfWhat the CM isn’t under a pivot gravity creates torque. is the axis of rotation? Is there a net force? What lever arm? Does is thethe normal force from the pivot create torque? Is there a net torque? A 6 meter long board has a weight of 800 N. If a fulcrum is placed under it 2 m from one end, what is the torque on it. What torque does gravity create on a .35 kg meterstick which is supported at the 15 cm mark? Fg Find the center of rotation (pivot point) Find the lever arm Force Fg The object below does not fall over (rotating around its base) Because there is NO TORQUE What is the lever arm in these examples? Fg Force If the object is tilted more, which has more torque on it due to gravity? Fg Fg Fg Gravity exerts a torque Will the object fall now? Fg A Net force causes an object to… A Net Torque causes an object to… When a football is kicked where is the axis of rotation? Through the center of mass! Can you kick a foot ball so the it does not rotate (end over end)? When a force is applied through the CM. Will it accelerate? YES Will it rotate? Is there torque? What about here-Will it accelerate? YES Will it rotate- Is there torque YES Will it accelerate? YES Will it rotate? Hoverpuck Demos A ball usually starts to rotate as is rolls down a hill If there was no friction would a ball still spin as it went down a hill? Is the force of gravity causing a torque? Fg FN Fg Will the normal force cause a torque? What else is acting on the ball Will friction cause the ball to rotate? FF FN Fg Free body diagrams Rolling Down a Hill Sliding w/o Friction FN FN FF FgX FgX FgY FgY Notice that freebody diagrams are not helpful for determining torque only if a body will accelerate Objects at equilibrium are perfectly stationary We may observe 2 things Their velocity remains 0 They do not rotate In order for an object to be perfectly still or at equilibrium, 2 Conditions MUST BE MET #1 All FORCES must cancel #2 All TORQUES must cancel Is there a Net force on the object? A Net Torque? 100 N This meter stick will only rotate... 100 N Will this object translate or rotate? Consider the CM the axis of rotation 100 N 100 N Will this object accelerate or rotate? 100 N 100 N Will this object accelerate or rotate? 100 N 100 N 100 N Will this object accelerate or rotate? 100 N 200 N 100 N Will this object accelerate or rotate? 100 N 50 N Will this object accelerate or rotate? 100 N 50 N Will this object accelerate or rotate? 100 N 50 N Will this object translate or rotate? 100 N 150 N 50 N A 150 N person stands in the middle of 2 scales on a board, what does each read? 150 N 75 N Do forces cancel? Do torques cancel? 75 N Where should a person stand so that 1 scale reads 30 Newtons? Forces must cancel Torques must cancel 30 N 4d 1/4 the force of the other side So 4 x the lever arm 150 N d 120 N What if a 150 N person stands 1/3 away from one scale? 150 N 50 N 1d 2d 1/3 distance 2/3 force Consider the person the axis of rotation 100 N Example calculation of meterstick practicuum lab A meterstick has a mass of 124 g and its center of mass is at the 56.1 cm mark. If the fulcrum is placed at the 64 cm mark, where should a 75 g mass be hung for it to balance? Torque and CM WS Meterstick Practicum Page 365 7-15 Let’s rewrite Newton’s 1st law of motion Linear An object will only change velocity if a Net Force is applied. No net Force = keeps moving at the same speed Rotational An object will only change its Rotational speed if a Net Torque is applied. No net Torque = keeps rotating at the same speed Demo- Raw vs Hardboiled eggs The property of mass to resist a change in motion is INERTIA OBJECTS HAVE BOTH: Linear Inertia: & Rotational Inertia Picture yourself running and pushing a merry go round full of your friends verses and empty one. The more people that are on it, the harder it is to spin!!! (and to slow down) The more mass on the merry go round the more it resists changing its ROTATIONAL speed. Rotational Inertia: --resistance to rotational acceleration -- depends not just on how much mass but also the location of the mass Demo- rotating a stick Try waggling your leg fully extended vs. with your knees bent Location, location, location The further the mass is from the pivot point, the more the ROTATIONAL INERTIA If both have the same mass will they be the same difficulty to spin? The ROTATIONAL INERTIA also depends on how the object is being spun (the axis of rotation) Which has the higher rotational inertia A baseball bat is harder to swing if held from the end And harder to slowdown A tennis racket can pivot through several axes, which will be the EASIEST (lowest rotational inertia) Hardest Easiest Consider a disc, how will it be easier to rotate? (neglecting air resistance) Like a record Flat Demo: Rolling Race Two discs with the same mass and radius are rolled down a hill. One is hollow and the other solid? Which will make it to the bottom first or will it be a tie? Pipe same mass diff diameter PVC/PVC Pipe same diameter diff mass (same length) PVC Steel Mass is concentrated towards the edge away from center of rotation. Higher rotational inertia Mass is distributed uniformly Rotational Inertia --symbol is: I --units are: kg m2 --depends on Shape, Mass, Axis of rotation (see page 157) but here are a few for examples Hoop spinning like a record Hoop spinning flat I = mr2 I = 1/2 mr2 (see page 223 Honors text) but here are a few for examples r Rod I = mr2 2 rotating through center of circle L Rod I = mL2 12 rotating through CM L Rod rotating about an end I = mL2 3 What is the rotational inertia of a 1.0 kg board that is .86 m long being swung at its end vs. its middle? .86 m Weight pulls it down the slope Friction gets it rotating working against rotational inertia NEWTONS 2nd Law Linear Motion F = ma Rotational Motion t= I a Rotational Motion t= I a For a given object (I) t a the greater the torque, the faster its spin speeds up Rotational Motion t= I a For a given torque (t) I a For a given torque, the bigger the rotational inertia the slower it will spin rate will change 2 block and tackle systems have 500 g masses attached. Compare their rotational accelerations more t = more a If each is pushed with the same force on the edge, which will accelerate faster? Recall Momentum Two Pieces - Inertia & Speed Momentum = mass x velocity p = mv Roughly how hard it will be to get something to stop moving But an object can also have ROTATIONAL MOMENTUM Roughly how hard it is to get an object to stop rotating. It also depends on TWO things Linear Momentum Rotational Momentum r = mv L = _I _w Rotational Inertia rotational velocity If the disks are equal which has the greater rotational momentum Greater rotational velocity, more momentum The disks are rotating at the same speed, Which has more momentum Thick disk Greater I = more momentum Thin disk A disk and a ring of equal mass are spinning at the same rate, which has more momentum Greater I = more momentum LINEAR MOMENTUM of a system is conserved if there are no external FORCES. p = mv linear momentum. Rotational Momentum is also conserved if there are no external______________ TORQUES Initial = Final L1 = L 2 I1w1 = I2w2 Consider an ice skater. If nothing exerts a torque on her while doing a spin (friction on ice / wind resistance / angry fan) her rotational inertia is constant I0w0 = Ifwf BUT WHY does she spin faster when she brings her arms in? Remember rotational inertia depends on two things How much mass How far the mass is from the axis of rotation. The mass of the skater doesn’t change BUT it can be placed further or closer to the rotational axis. (If the skater starts at the left position. How will their rotational speed change) Start SLOWER FASTER FASTER SLOWER Iw 0 0 w = If f A tucked diver spins at 1 rotations per second. If she extends herself quadrupling her rotational inertia, what is her rotational speed? Chair Demo Is rotational momentum conserved if an external force is applied? A diver can control their angle of entry by controlling their rate of rotation What happens to the speed of the merry go round if if start in the middle and go to the outside? Will you be traveling faster or slower or the same? Linear Momentum has a direction (same as velocity) Positive velocity Positive momentum Negative velocity Negative momentum Rotational Momentum also has a direction (like linear momentum) The vector direction is a little weird and we don’t need to memorize this but it points through the axis of rotation. Changing the axis of rotation changes the direction of its rotational momentum If the speed of a record 33 rpm clockwise, and it is spun at 33 rpm Counter-clockwise. Its momentum changed by a factor of: TWO This is like an bouncing backwards The rotational momentum resists changing direction. JUST like it is hard to get a semi truck going 60 mph N to go 60 mph S. The greater the I & the faster is spins-the harder it is to change This is what makes a top stable but only while it is spinning. Due to its center of mass it would otherwise not be stable Even better than a top is a: Gyroscope bicycle wheel, flip n flyer This is what also makes your bicycle easy to ride (while moving) If the boy is moving forward what is the direction of the momentum vector. (left or right) Demo: Bicycle wheel The total momentum of a “system” remains constant. (no outside torque) Two disks at rest The initial momentum is 0 If a person start pushing the top disc clockwise The bottom disc will move counter clockwise The momentum will be equal and opposite When a helicopter starts bringing its rotors up to speed, what happens? If global warming causes the polar ice to melt and flow towards the equator, what affect will this have on the earth’s rotation. How will this affect how long a day is? Book problems page 165-167 17, 18, 19, 20, 27, 30, 31, 32, 35, 36 A day at the Races (part I) (Rotational Momentum/Energy Lab) Which shape should be the best for rolling races? pipe solid sphere solid cylinder I = mr2 I = 2/5 mr2 I = 1/2 mr2 Which shape should be the best for rolling races? solid sphere solid cylinder pipe I = 2/5 mr2 I = 1/2 mr2 hollow sphere 2 I = 2/3 mr I= 2 mr How does mass affect the outcome of a rolling race? How does mass affect the outcome of “falling race” How does radius affect the outcome of “rolling race” How can these sportbikes lean at such impossible angles without falling over. THINK Center of Gravity, Centripetal Force, & Torque Any object which is rotating possesses: ROTATIONAL KINETIC ENERGY Think of any real examples of how rotational kinetic energy is used or what it does? Turbines generators Flywheels Tornado Flywheel Charge Time Energy / kg Problems 15 minutes 470 kJ Explosion Battery 8 hours 180 kJ Haz Materials Water Molecules and a Microwave How rotating water speed up Kinetic Energy Linear (translation) Rotation mv2 KEtrans = 2 KErot = I w2 2 Which type of kinetic energy does a rolling ball possess? rotational / kinetic / both BOTH Rolling animation