AP Physics C

1
AP Physics C

• Math Review

2
Vector Components

• All vectors can be broken into their individual x
  y components.
• Typically -
• However, if you have an inclined plane this will
  not be the case. Make sure you determine the x
  y components with the angles in your diagrams.

3
Vector Addition

• Break vectors into x y components
• Add the components together
• Report answer using magnitude and direction or
  components.
• î j are used to represent x and y
• You will use vector addition in kinematics, with
  forces, momentum, electric and magnetic field,
  and anything else that is a vector.
• Energy and electric potential are not vectors

4
Vector MultiplicationDot Product

• If we want the parallel components of two vectors
  we use the dot product.
• We use the cosine of the angle between the two
  vectors. Work is shown below
• Dot product is used with work, power (PFv),
  electric and magnetic flux, and Amperes Law.

5
Vector MultiplicationCross Product

• If we want the perpendicular components of two
  vectors we use the dot product.
• We use the sine of the angle between the two
  vectors. Torque is shown below
• Cross product is used with torque, angular
  momentum, magnetic force (for both a charge and a
  current)
• Direction is given by right hand rule. Index
  finger points in the direction of the first
  variable, middle finger with the second variable
  and the thumb is the direction of the result.

6
Differential Equations

• Differential equations are used to solve for
  objects that experience air resistance, harmonic
  motion, RL circuits, RC circuits, LC circuits

7
Differential EquationsRetarding Force (air
resistance)
Falling Object
Moving Forward

• Use Newtons Second Law and identify the forces
  on the object.
• Separate variables and integrate to solve. Be
  sure to include limits of integration
• You will end with something like e-kx or A(1 -
  e-kx )

8
Harmonic Motion

• The motion is periodic it repeats itself and
  can be modeled as a sine function
• Springs and LC circuits all have the same form.
• Pendulums are also harmonic

LC Circuit
Spring
9
RC CircuitsCharging

• Use Kirchoffs Loop rule to find voltage across
  each component. Set the current to dq/dt.
• Separate the variables and solve for q.

e
C
R
10
RL CircuitsRise of Current

• Use the same approach as the RC circuit the
  difference is that we look at current instead of
  charge.

11
Integration for AP Physics

• There are many cases where you will be asked to
  integrate on the AP Physics exam or when you are
  asked to find the area under a curve.
• The next few slides will deal with the more
  difficult integration that you may encounter.
• There are some common themes among Center of
  Mass, Rotational Inertia, Electric Field and
  Electric Potential

12
Integration for AP Physics

• For the situations listed in the last slide there
  are some common strategies to approach the
  problems.
• Identify symmetry and choose your axes so that
  you integrate along a line of symmetry
• Use the mass/charge density and break your object
  into pieces that fit the shape.

13
Integration for AP PhysicsLinear

• Break the long, thin rod into small pieces dx
• Use the mass/charge density to find dm or dq in
  terms of dx.
• Substitute in order to get a single variable in
  your integral
• Plug values in, set limits of integration and go

14
Integration for AP PhysicsTwo Dimensional

• Break the area into shapes either rings or
  rectangles
• Use the mass/charge density to solve for dm or dq
  in your ring
• Substitute in order to get a single variable in
  your integral
• Plug values in, set limits of integration and go

15
Integration for AP PhysicsThree Dimensional

• Break the area into shapes a sphere breaks into
  spherical shells. A cylinder breaks into
  cylindrical shells.
• Use the mass/charge density to solve for dm or dq
  in your shape
• Substitute in order to get a single variable in
  your integral
• Plug values in, set limits of integration and go

16
IntegrationOther Notes

• E-fields are vectors and you need to keep the
  direction in mind as you solve
• Center of Mass, Rotational Inertia and Potential
  are scalar quantities