315 Gausss Law
Note: Gausss Law is needed for AP Physics C: physical science majors, calculus based.
Flux: The amount of a field (gravity, electricity, or magnetism) passing through a defined area of space.
=(Field Strength)(Area) . Fields are visualized
18 Linear Momentum and Collisions
Momentum: p = mv Quantity of motion (inertia in motion). Measure of how difficult it is to stop an object.
Impulse: J = =F t p Trade off between time taken to stop and force needed to stop. Velocity,
acceleration, and mom
111 Rotation Detailed, Rolling, and Angular Momentum
Note: This detail on rotation is needed for AP Physics C: physical science majors, calculus
based.
Center of Mass: Objects rotate around a central axis and around a center of mass. It is therefore impor
19 Uniform Circular Motion and Gravity
Frequency: How often a repeating event happens. Measured in revolutions per second. Period:
1 in the numerator.
The time for one revolution. Time is
T=
v
Velocity: Direction and thus velocity are continuously changin
Example 9-7: Superposition of Gravity Fields
Superposition is a term referring to the addition, or superimposing, of two or more force fields. In Fig 9.7a mass A and mass
B both create gravity at all points in space to infinity. If an object is positioned
Example 8-2: Two dimensional Collision
before and two after. mv1 1ix +m
4m/s
1
Mass 1, m1 = 2kg, is moving at 4m/s to the right. Mass 2, m2 = 1kg, is
stationary and is hit by mass 1 just a little off center. This causes mass 2 to move
a 3m/s at an angle o
Power: Power is the rate of work, or rate of energy change. In other words it is the rate that energy is used,
transferred, or generated during a one second interval. Since it involves energy, power is by extension as important.
W
P=
Fr
P=
you can substit
Potential Energy: The energy of position. This time we are working with a springs position, . When a
spring is at equilibrium it is at rest and has zero displacement. This position is thus has zero potential energy. This
is just like gravitational potenti
Example 5-8: A Complex Slope Problem
Objects can move up or down a slope. F g sin is simply the component of gravity pulling on an object down the slope in a
direction parallel to the slope. In Fig 5.8a a man is pushing mass B up a slope. In this case gra
Example 6-2: Work and Potential Energy
Lifting a Mass: In order to lift a mass at constant velocity a force must be directed upward and be equal to the force
W = F rcos. Substitute Fg for F and height h for r. W =F hg cos. The force and
displacement are i
Example 6-1: Various Orientations of Force and Displacement.
In the first three scenarios a force F = 5 N acts on a mass which is displaced r = 2 m.
1
Force vector is parallel to the displacement vector and points in the same direction:
F
r
= 0o
F
W = r
Force Gravity on Slopes: Motion on a slope is parallel to the slope.
Direction
of motion
Fg is then at an angle to this motion. Any vector at an angle to motion
should be split into components parallel and perpendicular to the chosen
orientation (directio
Normal Force
Weight (also called force of gravity) is a pervasive force that acts at all times and must be counteracted to keep an object from falling. You
definitely notice that you must support the weight of a heavy object by pushing up on it when you h
Work is the Area Under the Force Displacement Curve
This is the integral of the force distance function in the calculus based course. In the non-calculus
course these areas will be simple enough (squares, rectangles, and triangles) to allow us to use geom
Example 8-2: Two dimensional Collision
4m/s
1
Mass 1, m1 = 2kg, is moving at 4m/s to the right. Mass 2, m2 = 1kg, is stationary and is
hit by mass 1 just a little off center. This causes mass 2 to move a 3m/s at an angle of 20o
below the x-axis. The colli
Compound Bodies in Two Dimensions: These problems have two or more masses
Direction of Motion
connected by a strings and involve pulleys. Pulleys are devices that change the direction of
force. The pulleys in the following examples will be considered mass
19 Uniform Circular Motion and Gravity
Frequency: How often a repeating event happens. Measured in revolutions per second.
Period: The time for one revolution. T = 1 Time is in the numerator.
f
v
Velocity: Direction and thus velocity are continuously chan
Example 5-7: Two Dimension Compound Body with Friction
A
Solve for acceleration: This is a repeat of Example 5-4, only this time friction appears in
the FBD for mass A. Friction opposes motion and is therefore negative.
m g mA g
a= B
( mA + mB )
( mA + mB
Force Gravity on Slopes: Motion on a slope is parallel to the slope. Fg is then at an
angle to this motion. Any vector at an angle to motion should be split into components
parallel and perpendicular to the chosen orientation (direction of motion). In thi
Pendulums: Approximates a Simple Harmonic Oscillator (SHO)
Restoring force: The restoring force is the sum of the tension and gravity vectors
diagramed to the right. When the object is at its extreme displacement (+x or x)
the restoring force is greatest.
18 Linear Momentum and Collisions
Momentum: p = mv Quantity of motion (inertia in motion). Measure of how difficult it is to stop an object.
Impulse: J = Ft = p Trade off between time taken to stop and force needed to stop. Velocity, acceleration, and
mom
16 Work, Energy, and Power
Work: Force applied to an object that moves a distance.
W = Fir = F r cos
is the angle between direction of motion and applied force.
Work is a Scalar (Dot) Product: The dot product (AB) of two vectors A and B is a scalar and
110 Introduction to Rotation and Torque
Rotation: In rotation the entire object spins around its center of mass. Looking at the tangential velocities diagramed at the
right, we see that they are all in different directions and all vary in magnitude. Point
The wheel to the left shows all the energies learned in this
class around the outside. They are grouped into the five
major strands of physics. In the center is work.
Newtonian Mechanics
K=
1
U s = kx 2
2
1 2
mv
2
U g = mgh
Ug =
E = hf
Modern
Physics
E=
W
further than the lowest height (zero potential energy), it can only loose this much potential energy. We are really just
tracking changes in usable energy. This is why Work and Work-Energy Theorem is such a useful entity.
20 J of work were added to the sy
Example 9-6: Gravity on an Unknown Planet
Mars has roughly half the radius of Earth and has one-tenth the mass.
What is the gravity on the surface of Mars? Many students want to look up the radius and mass of Mars and plug into this
m
. But there is anoth
Power: Power is the rate of work, or rate of energy change. In other words it is the rate that energy is used, transferred, or
generated during a one second interval. Since it involves energy, power is by extension as important.
P=
W
t
you can substitute
Example 9-4: Conical Pendulum
m1 is suspended by a string that passes through a tube. At the other end of the tube m2 is
hanging from the same string. m1 is spun at a velocity that keeps m2 stationary.
T = Fg2
Solve for the force centripetal. Force centri