1. Newton’s Laws
1st Law: A body acted on by no net force moves with constant velocity (which may be zero)
2st Law: The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object.
3rd Law: For every action there is an equal, but opposite reaction

2. The First Law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. It may be seen as a statement about inertia, that objects will remain in their state of motion unless a force acts to change the motion.

3. Aristotle: a natural state of an object is at rest; a force is necessary to keep an object in motion. It follows from common sense.
B.C.
Galileo: was able to identify a hidden force of friction behind common-sense experiments, abstracted from it a fundamental law of inertia and the principle of relativity

4. First Law is identical to Galilean Principle of relativity
Galileo Galilei
Galilean principle of relativity (Galileo’s ship!)
Laws of physics look the same for all observers who move with a constant velocity with respect to each other, i.e. in all inertial frames of reference.
Indeed, if no force in needed to keep the body in motion with constant velocity, all such states of motion are equivalent. For different inertial observers the object will appear moving with different but constant velocity (which may be zero).

5. The First Law contains implications about the fundamental symmetry of the universe in that a state of motion in a straight line must be just as "natural" as being at rest. If an object is at rest in one frame of reference, it will appear to be moving in a straight line to an observer in a reference frame which is moving by the object. There is no way to say which reference frame is "special", so all constant velocity reference frames must be equivalent.
The first law is valid only with respect to an inertial observer, i.e. in inertial frames of reference. It is violated in accelerated reference frames.

6. 2nd Law From experiments we know:
A force is needed to change the state of motion
Force is a vector; obeys superposition principle: the net force is a vector sum of all forces acting on an object
The direction of acceleration vector is the same as the direction of the force vector
The magnitude of the force and acceleration are related by a constant which intuitively is a “quantity of matter”. This is the inertial mass.

7. Newton’s 2nd Law of Motion
The acceleration a of a body is inversely proportional to its mass m, directly proportional to the net force F, and in the same direction as the net force.
a = F/m  F = m a
1 N = 1 kg m/s2

8. Newton’s 3rd Law of Motion
To every action, there is an equal and opposite reaction.
The same force that is accelerating the boy forward, is accelerating the skateboard backward.

9. Clockwork universe
Newtonian mechanics was so beautiful and clear that people believed that it explained everything. They thought that everything in the Universe worked like a perfect clock obeying Newton’s laws. To predict what happens in future, you just need to specify the initial positions and velocities for all objects.

10. Types of forces Gravity and weight Normal force Friction
Tension and spring force
Contact versus long-range forces
All are manifestation of four Fundamental “forces”
Gravity
Electromagnetic
Strong
Weak

11. M Gravity is a strange force. It has a unique property:
All bodies in the same point in space experience the same acceleration!
Galileo, about 1600 m R M

12. Weight, “apparent weight”, the force of gravity, and the normal force
Riding an elevator

13. Units of Force One pound is 0.4536 kg
British system:
units of mass:
units of force:
One pound is kg
One pound is the weight of kg on the Earth

14. Box on an inclined plane
A box with mass m is placed on top of a frictionless incline with angle q and height H and is allowed to slide down.
What is the normal force?
What is the acceleration of the box?
What is the velocity of the box when it reaches the bottom? q

15. Kinetic: The friction force that slows things down
Two types of friction:
Kinetic: The friction force that slows things down
Static: The force that makes it hard to even get things moving

16. Refrigerator
If you push a refrigerator when there is no friction what happens?
In the real world what happens? Especially when it’s fully loaded and on a sticky kitchen floor?
When does static friction kick in?
When does kinetic friction kick in?

17. Friction
There is some maximum value the friction force can achieve, and once we apply a force greater than this maximum there is a net force on the object, so it accelerates.
The maximum of the force of friction varied linearly with the amount that the block pushes on the table.
 - coefficient of friction, is the vertical force exerted by the block on the table
The friction force only exists when there is another force trying to move an object

18. FFriction = mKineticFNormal
Kinetic Friction
For kinetic friction, it turns out that the larger the Normal Force the larger the friction. We can write
FFriction = mKineticFNormal
Here m is a constant
Warning:
THIS IS NOT A VECTOR EQUATION!

19. FFriction  mStaticFNormal
Static Friction
This is more complicated
For static friction, the friction force can vary
FFriction  mStaticFNormal
Example of the refrigerator:
If I don’t push, what is the static friction force?
What if I push a little?

20. Is it better to push or pull a sled?
You can pull or push a sled with the same force magnitude, FP, and angle Q, as shown in the figures.
Assuming the sled doesn’t leave the ground and has a constant coefficient of friction, m, which is better? FP FP

21. A Recipe for Solving Problems
Sketch
Isolate the body, draw a free-body diagram (only external forces but not forces that one part of the object exert on another part)
2. Write down 2nd Newton’s law
Choose a coordinate system
Write 2nd Newton’s law in component form:
3. Solve for acceleration

22. Pulling Against Friction
A box of mass m is on a surface with coefficient of kinetic and static friction m. You pull with constant force FP at angle Q. The box does not leave the surface.
Find the minimum force you need to apply in order to move the block
What is the magnitude of the acceleration?
What angle maximizes the acceleration? Q

23. Box on an inclined plane with friction
A box with mass m is placed on an incline with angle q and is allowed to slide down.
What is the acceleration of the box? q

24. Tension and pulleys

25. Force of tension
Massless, unstretchable string; massless, frictionless pulley

27. The advantage of a pulley
What minimum force F is needed to lift the piano of mass M?

28. Conical pendulum

29. A ball of mass m is swung around a circle at the end of a string of length L. The string will break if the tension in it exceeds a critical value, Tc.
What is the largest constant angular velocity the ball can have without breaking the string?
What is the largest period the ball can have without the string becoming slack?

30. A mass m1 is going around in a circle on a string on a frictionless table and the string goes through a hole where it is attached to a hanging mass m2. If the mass m1 is going around with constant , what must the distance from the mass m1 to the hole be if the mass m2 is to remain at rest? m1 m2

31. Playing with weight: A car on an arched bridge
Your weight in a rotating space station
or on the rotating Earth

32. A race track designer wants to have the cars able to maintain a speed vmax without skidding on a circular track. If the track is flat with a coefficient of friction  what does the radius have to be?
A race track designer wants to have the cars able to maintain a speed vmax without skidding. At what angle must the track of radius R be banked assuming no friction? Assuming a coefficient of friction ?

33. A satellite of mass m is attracted to the Earth of mass M with a force of gravity proportional to the inverse square of the distance to the Earth center, r:
 is a gravitational constant
Find the velocity of a satellite on circular orbit of radius r.
Find the radius of the orbit for a geostationary satellite