1. Motion in Two Dimensions
Finding the net direction of two motions
Use Pythagorean Theorem to find the magnitude of the resultant vector
Use the tangent function to find the direction (angle) of resultant motion
tan θ = opp/adj
θ = tan-1(opp/adj)

2. Motion in Two Dimensions
Resolving a vector into components
The horizontal component is the vector (here = F) times cos θ
The vertical component is the vector (again = F) time sin θ

3. Projectile Motion Launched horizontally (cliff top)
Horizontal motion is uniform motion (no acceleration)
vx,I = vx,t = vx,f = constant
Vertical motion is uniform accelerated motion
Use equations for falling objects!!
Link H + V motion with time

4. Projectile Motion Launched at an angle (full parabola)
Initial velocity is at an angle (the resultant vector)
Find the horizontal and vertical components of the initial velocity
Horizontal motion is still at constant velocity!
Vertical motion is still at constant acceleration!
Continue to use time to link horizontal and vertical motion!

5. Uniform Circular Motion
Recall that velocity is described by magnitude (speed) and direction.
Sometimes the acceleration an object experiences changes its direction and not its speed.
This occurs in uniform circular motion – circular motion at a constant (tangential) velocity
Objects in uniform circular motion experience “centripetal” acceleration
This acceleration is directed from the object into the center of the circle

6. Centripetal Acceleration
Centripetal acceleration is
Proportional to the square of the tangential velocity
Inversely proportional to the radius of the circle
ac = v2 / r

7. Centripetal Force If Force = mass x acceleration…
Centripetal force = mass x centripetal acceleration
Fc = m v2 / r
Centripetal force is also directed toward the center of circular motion

8. Implications
If the centripetal acceleration/force is removed, the object will move in the direction of its tangential velocity
Centripetal force (due to the sun’s gravity) keeps Earth in its orbit