Two Dimensional Kinematics  

Vectors

• Quantities with both magnitude and direction

• Magnitude is a number value (with units)

• Directions can be compass points, left, right, up, down, etc.

• You can assume that every vector makes a right angle. You can use trigonometry to find the resultant vector (R).

• This is the sum of both vectors.

• To subtract a vector you add the negative of that vector.

• The negative of that vector has an opposite direction (180)

Projectile Motion

• Projectile motion describes objects travelling through space under the influence of gravity

• This applies from when the object is launched to right before it hits the ground

• ==The only force is the weight (force of gravity)==

• Ay = -9.80 m/s

• Ax = 0 m/s

• In the X-Axis we can only use the equation vx = x/t

• In the Y-Axis we can use 4 kinematic equations:

  

• The easiest way to solve for projectile motion is to use a table!

• Example: If a projectile was launched at 22 m/s at an angle of 35 what is the displacment after 2.50s?

• The displacement can now be solved for using vector trigonometry

• Take the square root of 45^2 and .88^2 = 45m

Uniform Circular Motion

• Uniform circular motion describes objects moving in a circular path with a constant speed. The magnitude of the velocity is a constant.

• At any moment the direction of the velocity is tangent to the path that it is following

• This is called the tangential velocity

• The magnitude can be found using: v = d/t → 2πr/T

• ==Acceleration can cause a change in direction but does not change the magnitude of the velocity==

• It is always directed towards the center of the path

• Centripetal means directed to the center

• Centripetal acceleration can be found using v^2/r

• Example: A car traveling at 25.0 m/s around a curve with radius 15 meters

• If we were to find the centripetal acceleration we use Ac = v^2/r

• Ac = 25^2/15 = 42 m/s