Today: Finish Newton’s laws, Linear and Angular Momentum Newton’s Cradle: Dominique Toussaint on wikipedia

Exam #3 curved results

FORCE …What is a force? What can force do? Force changes the motion of an object gravitational force is responsible for the elliptical orbit of the Earth / Sun. frictional force slows down a sliding hockey puck. Force causes deformations in an object electrical force causes nucleus to deform applied force can cause a spring to stretch or compress

What can force do?

Force changes the motion of an object

gravitational force is responsible for the elliptical orbit of the Earth / Sun.

frictional force slows down a sliding hockey puck.

Force causes deformations in an object

electrical force causes nucleus to deform

applied force can cause a spring to stretch or compress

FORCE …What is a force? What kind of forces are there? Fundamental: Gravity, Electromagnetic, strong, weak Practical: Gravitational, electrical, magnetic, frictional, drag “stretchy”, contact (hard objects) All of these can be measured in units of “force” Pounds or Newtons are common. 2.2 lbs. =~ 10 Newtons. (1 kg weighs 10 Newtons on Earth)

What kind of forces are there?

Fundamental: Gravity, Electromagnetic, strong, weak

Practical: Gravitational, electrical, magnetic, frictional, drag “stretchy”, contact (hard objects)

All of these can be measured in units of “force”

Pounds or Newtons are common. 2.2 lbs. =~ 10 Newtons. (1 kg weighs 10 Newtons on Earth)

A little bit about “net force” Forces have a directionality “ Net Income” = profit after adding up all the plusses and minuses. “ Net Force” = force after adding up all the up, down, left, right and diagonal force vectors Zero 10 Lbs 10 Lbs “ 10 Lbs up + 10 Lbs down = zero net force” 10 Lbs 45 deg. up 10 Lbs 45 deg. down “ 10 pounds up and to the right + 10 pounds down and to the right = 14 pounds to the right” 14 lbs right

Forces have a directionality

“ Net Income” = profit after adding up all the plusses and minuses.

“ Net Force” = force after adding up all the up, down, left, right and diagonal force vectors

Newton’s three laws of motion: review of 1 st two 1. Inertia: An object’s motion will not change unless acted on by an external force. Acceleration is proportional to force. a = F / m

1. Inertia: An object’s motion will not change unless acted on by an external force.

Acceleration is proportional to force. a = F / m

Let’s look some more at Newton’s first two laws, and inertia http://www.youtube.com/watch?v=Hyw9uNF4nmE&feature=related (excellent lecture on inertia) (Last week we did some of our own lecture demos (table cloth, smashing hand)) And watch this famous demo: http://www.youtube.com/watch?v=_TKe5rBJeYc

Newton’s third law of motion . “ When two objects interact, the forces they exert on each other are equal and opposite” “ For every action, there is an equal and opposite reaction.” “ For an isolated system , there is conservation of momentum ” The Sun cannot attract the Earth without the Earth attracting the sun…You cannot push on the bumper of a car without the bumper of the car pushing on you. Force Force http://www.youtube.com/watch?v=8deNwoczCPc&feature=related Canon recoil

“ When two objects interact, the forces they exert on each other are equal and opposite”

“ For every action, there is an equal and opposite reaction.”

“ For an isolated system , there is conservation of momentum ”

The Sun cannot attract the Earth without the Earth attracting the sun…You cannot push on the bumper of a car without the bumper of the car pushing on you.

Linear Momentum Also just referred to as “momentum” Momentum is proportional to mass Momentum is proportional to velocity (speed) Momentum is a vector (we won’t use these) Momentum = mass x velocity p =m v Like total energy , linear momentum is conserved…cannot be created or destroyed. Conservation of momentum is reflected in Newton’s 1 st and 3 rd laws. Force Force http://canu.ucalgary.ca/map/content/force/newton3/exploding_blocks/applet.html

Also just referred to as “momentum”

Momentum is proportional to mass

Momentum is proportional to velocity (speed)

Momentum is a vector (we won’t use these)

Momentum = mass x velocity

p =m v

Like total energy , linear momentum is conserved…cannot be created or destroyed.

Conservation of momentum is reflected in Newton’s 1 st and 3 rd laws.

Let’s think about conservation of momentum Newton’s cradle demo Momentum conserved, kinetic energy NOT conserved. momentum = mass * velocity kinetic energy = ½ mass * (velocity) 2 “ Elastic collision” total kinetic energy conserved “ inelastic collision” kinetic energy lost via heat flow Newton’s Cradle: Dominique Toussaint on wikipedia

Newton’s cradle demo

Momentum conserved, kinetic energy NOT conserved.

momentum = mass * velocity

kinetic energy = ½ mass * (velocity) 2

Brainstorming session Part 1 – Think of examples where linear momentum appears to NOT be conserved Throwing clay at the wall; Car crash—inelastic collision car smashing into steel pole; bullet into bullet proof vest; bird against the window; skier into tree; drop something onto the ground; Part 2 – one object was at rest other in motion, both end up at rest; objects change shape (accounts for the inelasticity or loss of kinetic energy); always a smaller object crashing into a much bigger object.

Clicker question—conservation of momentum Consider a car at rest at a stop light. When the light turns green, the car accelerates up to a speed of 60 mph. The momentum went from zero to something much more than zero! Does this violate the law of conservation of momentum??? Yes No

Consider a car at rest at a stop light. When the light turns green, the car accelerates up to a speed of 60 mph. The momentum went from zero to something much more than zero! Does this violate the law of conservation of momentum???

Yes

No

Clicker question—conservation of momentum Consider a car at rest at a stop light. When the light turns green, the car accelerates up to a speed of 60 mph. The momentum went from zero to something much more than zero! Does this violate the law of conservation of momentum??? Yes No It really is a very good law of physics, so has to be “no.” But where did the momentum come from?

Consider a car at rest at a stop light. When the light turns green, the car accelerates up to a speed of 60 mph. The momentum went from zero to something much more than zero! Does this violate the law of conservation of momentum???

Yes

No

Angular momentum is the momentum of spinning or orbiting. For linear momentum, recall: Momentum is proportional to mass Momentum is proportional to velocity (speed) momentum = mass x velocity momentum = inertia x velocity Angular momentum is similar: Angular momentum is proportional to rotational inertia Angular momentum is proportional to rotational speed angular momentum = rotational speed x moment of inertia Complicated!!!

For linear momentum, recall:

Momentum is proportional to mass

Momentum is proportional to velocity (speed)

momentum = mass x velocity

momentum = inertia x velocity

Angular momentum is similar:

Angular momentum is proportional to rotational inertia

Angular momentum is proportional to rotational speed

angular momentum = rotational speed x moment of inertia

Complicated!!!

Moment of inertia (rotational “mass”) The further the mass from the rotation axis, the higher the moment of inertia. angular momentum = rotational speed x moment of inertia

The further the mass from the rotation axis, the higher the moment of inertia.

angular momentum = rotational speed x moment of inertia

Clicker Question—Angular Momentum Two spinning tops have exactly the same mass and are spinning at exactly the same angular rate (e.g., 1000 rpm). Which of them would have more angular momentum? A B C Exactly the Same

Two spinning tops have exactly the same mass and are spinning at exactly the same angular rate (e.g., 1000 rpm). Which of them would have more angular momentum?

Clicker Question—Angular Momentum Two spinning tops have exactly the same mass and are spinning at exactly the same angular rate (e.g., 1000 rpm). Which of them would have more angular momentum? A B C Exactly the Same Mass farther away from axis contributes more to angular momentum

Two spinning tops have exactly the same mass and are spinning at exactly the same angular rate (e.g., 1000 rpm). Which of them would have more angular momentum?

Angular momentum is conserved also! Like total energy and linear momentum, there is “conservation of angular momentum”…cannot be created or destroyed If two objects are spinning in opposite directions, they have opposite angular momentum. “ right hand rule” Angular momentum “up” “ positive”, “spin up” Angular momentum “down” “ negative”, “spin down”

Like total energy and linear momentum, there is “conservation of angular momentum”…cannot be created or destroyed

If two objects are spinning in opposite directions, they have opposite angular momentum.

“ right hand rule”

Clicker question—”right hand rule” Say I spin a top on a table. Looking at the top from above, it is rotating counter-clockwise. Is this top “spin up” or “spin down”? spin up spin down View from above

Say I spin a top on a table. Looking at the top from above, it is rotating counter-clockwise. Is this top “spin up” or “spin down”?

spin up

spin down

Clicker question—”right hand rule” Say I spin a top on a table. Looking at the top from above, it is rotating counter-clockwise. Is this top “spin up” or “spin down”? spin up spin down View from above

Say I spin a top on a table. Looking at the top from above, it is rotating counter-clockwise. Is this top “spin up” or “spin down”?

spin up

spin down

Falling cat and angular momentum… Does this violate law of conservation of angular momentum?

First, I want to point out how dangerous this is. In this case, the falling cat JUST MISSED a sleeping baby!!! Cat shaped hole in mattress Oblivious sleeping baby

Falling cat does not violate conservation of angular momentum At beginning and end, cat has Zero angular momentum. In between it’s diffuclt to see, but total angular momentum still zero. We maybe can demonstrate this with the spinning chair???

Let’s play with some demos of “conservation of angular momentum!” Spinning chair / dumbells Bicycle wheel / chair

Spinning chair / dumbells

Bicycle wheel / chair