Classical mechanics: Newton’s laws of motion

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Occam’s razor

• Given two competing — and equally successful — explanations for an observed phenomenon, the simpler one is preferred

• This idea has really been taken to heart by scientists. The development of physics has largely been driven by the search for a small number of principles or equations that describe a huge range of phenomena

William of Occam1285-1347

Clicker question

Darwin's theory of evolution meets all the criteria of a good scientific theory. This means:A. Scientific opinion is about evenly split as to whether

evolution really happened.B. Scientific opinion is largely in favor of evolution. C. It is a simple theory that explains a wide variety of

phenomena, and it has met every scientific challenge to its validity.

D. There is no longer any doubt that the theory of evolution is absolutely true.

Clicker question

Darwin's theory of evolution meets all the criteria of a good scientific theory. This means:A. Scientific opinion is about evenly split as to whether

evolution really happened.B. Scientific opinion is largely in favor of evolution. C. It is a simple theory that explains a wide variety of

phenomena, and it has met every scientific challenge to its validity.

D. There is no longer any doubt that the theory of evolution is absolutely true.

Classical mechanics

The theory of classical mechanics (also often called “Newtonian mechanics”) is concerned with the motion of objects.

The word “classical” refers to the fact that it does not work at extremely high speeds nor in very strong gravitational fields (this is where you need the theory of relativity). It also does not work on very small scales (quantum mechanics).

Classical mechanics

• The theory of classical mechanics is an extremely good theory:• It works very well in the cases where we expect it to

(i.e. classical cases)• It is simple and powerful: it uses a very small

number of principles and equations to describe a very large range of phenomena

Basic concepts in movement

• speed — the distance travelled in a certain amount of time. (For example, a car driving at 60mph.)

• velocity — this refers to both the speed and the direction. (For example, a car driving north at 60mph has a different velocity than a car driving east at 60mph.)

• acceleration — a change in velocity. (So a car that is turning but maintaining a constant speed is accelerating. So is a car that is going in a straight line but is slowing down; this is negative acceleration)

Acceleration

Q: I toss a ball up in the air, and then catch it as it falls back down. Between the time that it leaves my hand and I catch it, at what point does it reach maximum speed?

A. The moment after it leaves my handB. The moment before it lands in my handC. When it reaches it’s highest point in the airD. The speed is constant throughoutE. Both A and B

Speed

Q: I toss a ball up in the air, and then catch it as it falls back down. Between the time that it leaves my hand and I catch it, at what point does it reach maximum speed?

A. The moment after it leaves my handB. The moment before it lands in my handC. When it reaches it’s highest point in the airD. The speed is constant throughoutE. Both A and B

Speed

Q: I toss a ball up in the air, and then catch it as it falls back down. Between the time that it leaves my hand and I catch it, at what point does it reach minimum speed?

A. The moment after it leaves my handB. The moment before it lands in my handC. When it reaches it’s highest point in the airD. The speed is constant throughoutE. Both A and B

Velocity

Q: I toss a ball up in the air, and then catch it as it falls back down. Between the time that it leaves my hand and I catch it, at what point does it reach minimum speed?

A. The moment after it leaves my handB. The moment before it lands in my handC. When it reaches it’s highest point in the airD. The speed is constant throughoutE. Both A and B

Speed

Q: I toss a ball up in the air, and then catch it as it falls back down. At what point does it reach maximum acceleration?

A. The moment after it leaves my handB. The moment before it lands in my handC. When it reaches it’s highest point in the airD. The acceleration is constant throughoutE. Both A and B

Acceleration

Q: I toss a ball up in the air, and then catch it as it falls back down. At what point does it reach maximum acceleration?

A. The moment after it leaves my handB. The moment before it lands in my handC. When it reaches it’s highest point in the airD. The acceleration is constant throughoutE. Both A and B

Acceleration

Isaac Newton, 1643-1727

• Probably the most important scientist in history

• Developed the three laws of motion and the ”universal” law of gravitation

• Is one of two people that invented calculus

Isaac Newton, 1643-1727

Newton’s first law (originally due to Galileo)

“A body at rest remains at rest and a body in motion continues to move at constant velocity along a straight line unless acted upon by an external force” (this is Galileo’s formulation)

This law may seem contrary to our everyday experience. But that’s because in our everyday experience, there are always the forces of gravity, friction, and air resistance at work

Newton’s first law

Q: A ball is rolling down a corkscrew-shaped slide. When the ball hits the ground, in what direction will it continue to move?

A. it will roll in a straight line, in whatever direction it was last moving when it exited the slide

B. it will roll along a curved path

Newton’s first law

Q: A ball is rolling down a corkscrew-shaped slide. When the ball hits the ground, in what direction will it continue to move?

A. it will roll in a straight line, in whatever direction it was last moving when it exited the slide

B. it will roll along a curved path

Newton’s second law

Force = mass x acceleration

F=ma

A force is just a push or a pull that causes something to accelerate, i.e. to change its velocity

Newton’s second law

Force = mass x acceleration

A good baseball player can throw a baseball over 200 feet, and the world record is well over 400 feet. In contrast, the world record in the shot put is 75 feet. Is this because baseball players are so much stronger than shot putters?

Newton’s second law

But what happens when you push on something, and it doesn’t move? Aren’t you applying a force?

F=ma

Newton’s second law

But what happens when you push on something, and it doesn’t move? Aren’t you applying a force?

F=ma

This is the net force. It’s possible for an object to feel a lot of forces from many different directions, but if they all cancel each other out then the net force is zero

Is a net force acting on each of the following? (yes or no)• A car coming to a stop• A bus speeding up• An elevator moving up at constant speed• A bicycle going around a curve• A moon orbiting Jupiter

Is a net force acting on each of the following? (yes or no)• A car coming to a stop: Yes• A bus speeding up: Yes• An elevator moving up at constant speed: No• A bicycle going around a curve: Yes• A moon orbiting Jupiter: Yes

Newton’s third law

• For every force, there is an equal and opposite force

Newton’s third law

• Speed, velocity, and acceleration

• Newton’s three laws of motion• An object at rest will remain at rest, and an object in

motion will remain in motion with constant velocity• Force = mass x acceleration• For every force, there is an equal and opposite force

• Speed, velocity, and acceleration

• Newton’s three laws of motion• An object at rest will remain at rest, and an object in

motion will remain in motion with constant velocity• Force = mass x acceleration• For every force, there is an equal and opposite force

• Momentum and angular momentum

• Energy

Momentum

• An object at rest will remain at rest, and an object in motion will remain in motion with constant velocity

• Why is this? Because of momentum!

• momentum = mass x velocity

• So we can re-state Newton’s first law as: an object’s momentum will not change unless a force is applied to it

Angular momentum

• There is also a “circling momentum”, or angular momentum

• A version of Newton’s first law also applies to angular momentum — an object’s angular momentum will not change unless some external force is applied

• This is why the Earth continues to orbit around the Sun, even though nothing is pushing it. And it’s why the Earth continues to spin.

Angular momentum

angular momentum = mass x velocity x distance

So, at fixed angular momentum, an object that is further away will move slower

Angular momentum

angular momentum = mass x velocity x distance

So, at fixed angular momentum, an object that is further away will move slower