1. MONDAY(09/14): Introduction to Motion in Two Dimensions (Ch. 4).

Deriving the equations. HW: Read pages 83-87 and solve prob. 10, 15, 19,

and 23 on pages 102-3.

2. TUESDAY(09/15): Uniform Circular Motion. HW: Read pages 87-91 and

solve prob. 25, 27, & 29 on page 104.

3. WEDNESDAY(09/16): Lab on Two Dimensional Motion. HW: Process

Lab Data.

4. THURSDAY(09/17): Post-Lab Discussion. HW: Complete lab report

and write Abstract, due Friday.

5. FRIDAY(09/18): Relative Velocity. HW: Read pages 91-96 and solve

prob. 33, 39, 41, & 42 on page 104-5.

6. MONDAY(09/21): Review for Ch.4. HW: Complete Review Handout.

7. TUESDAY(09/22): TEST on Ch.4 - Motion in Two Dimensions.

HW: Go to web-site for notes on Ch.5 - The Laws of Motion.

WEBSITE NOTES for AP Physics C: Ch.4 - Motion in Two Dimensions.

In two-dimensional motion, the horizontal and vertical components of the

motion must be regarded independently. For these two directions we use x

and y, respectively. For example, if an object is projected from the ground

with a velocity v_i at an angle of elevation θ_i, then we can use SOHCAHTOA

to find out how fast it is moving in the x and y directions.

1. An object launched from the ground at some angle θ_i is called a projectile.

The path it travels is an inverted parabola called its trajectory. A classic

example would be the motion of golf ball when struck with a club. Can you

think of a few more?

2. The initial velocity in the x direction is v_xi = v_i·cos(θ_i). The velocity of the

object in the y direction is v_yi = v_i·sin(θ_i). The acceleration is that of gravity

which acts only in the y direction. It is given by a_y= -g = -9.8m/s². The

acceleration in the x direction is a_x = 0.

3. We still have the five motion formulas from the study of kinematics

developed by Galileo (1564-1642). We know them as: (a) Δx = v_avg·Δt ,

(b) v_avg = (v_i+v_f)/2 , (c) v_f = v_i + a·Δt , (d) v_f² = v_i² + 2a·Δx ,

(e) Δx = v_i ·Δt + ½a·Δt² . The task now is to adjust these for the separate

x and y directions.

4. Doing this, we get the following set of kinematics equations to analyze the

motion of a projectile launched at an angle. For the x direction we only have

Δx = v_xi·Δt . For the y direction we have 3 equations: (a) v_yf = v_yi - g·Δt ,

(b) v_yf²  = v_yi² - 2g·Δy ,  and (c) Δy = v_yi ·Δt - ½g·(Δt)². 

5. In the absence of air resistance a projectile has a constant horizontal

velocity and a constant downward free-fall acceleration which effects the

vertical velocity, subtracting 9.8m/s from it on the way up, and adding

9.8 m/s to it on the way down.

6. A frame of reference is a coordinate system for specifying the precise

location of objects in space. Maybe you have heard the expression, "It

depends on your frame of reference."

7. To two observers moving relative to each other there would not be

agreement on the displacements and velocities of an object in motion when

 each is using his/her own frame of reference.

8. For example, a person standing in a moving subway car, and facing

towards the back of the car, drops a book. According to the frame of

reference of the person in the car, the book fell in a straight line to the floor.

An observer standing outside on the subway platform as the car goes by,

sees the book traveling in a parabolic path toward the floor.

9. Therefore, the motion of an object depends on your frame of reference.

This is also occurs when boats travel in moving streams and when planes

encounter moving air masses. Also, sometimes you hear about certain

records in track and field that are not allowed if it is determined that

athletes were "wind aided."

10. Another type of two-dimensional motion is periodic motion in which an

object moves back and forth over the same path. This would be a pendulum,

for example. Also included is uniform circular motion in which an object has a

constant speed and is accelerated toward the center of the circular path.

11. This introduces the concept of a centripetal (center seeking) acceleration,

a_c = v²/r , which we will derive in class. Also, if we need the time for one

12. If a particle moves along a curved path in such a way that the magnitude

and direction of v change with time, the particle has an acceleration vector

that can be described with two component vectors.

13. The radial component vector arises from the change in direction of v,

which is the centripetal acceleration, a_c = v²/r .

14. The tangential component vector is based on the change in magnitude

of v, and is found with the derivative a_t = dv/dt .

15. The total acceleration can be found with the vector sum of these two

accelerations which occur at right angles, so we use the Pythagorean

theorem and inverse tangent.

16. Make sure you use  these steps to solve any problem in Physics:

(i) read the problem and identify the given variables

(ii) determine what you are asked to solve for

(iii) find the correct vector formula to use

(iv) use Algebra, Trigonometry, and/or Calculus to isolate the unknown

(v) substitute-in the given information and simplify.