Ch C: Vectors and kinematics

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Ch C Vectors and kinematics

• I. Euclidian space, coordinates and reference
  frames
• II. The Displacement vector and vector
  properties
• III. Basis vectors and vector operations (dot
  and cross products)
• IV. Velocity and Acceleration
• V. Uniformly accelerated motion
• VI Uniform Circular Motion

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• I. Euclidian space, coordinates and reference
  frames

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• II. The Displacement vector and vector
  properties
• Definition
• Components
• Arrow representation

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• II. The Displacement vector and vector
  properties
• Properties
• multiplication by number (incl neg)
• Addition

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• III. Basis vectors and vector operations (dot
  and cross products)
• Definitions

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oops

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• III. Basis vectors and vector operations (dot
  and cross products)
• Dot product
• Cross Product

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IV. Position, Velocity, Acceleration Definitions

• Position
• Velocity
• Acceleration

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Uniformly Accelerated Motion (U.A.M.)
Which of the following accelerations are
constant? A yes, constant B not constant
C maybe constant
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U.A.M. 1dim (say x-axis) Velocity, Position

• Velocity
• Position

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Try to find the sign of x, v, a for these
exercises A Positive B Negative C
Cannot be determined
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Uniformly accelerated motion (more than 1 dim)

• Choose 1 axis // to the acc. (say x-axis)
• Write down the kinematics equations for all axes
• Solve
• Here for 2 dim

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Free Fall in 1 dim.

• Typical problem How high does the ball go,
  after throwing it upward at v10m/s
• Solution
• Draw picture
• Write relevant equations
• Write constraint equation(s)
• Solve for unknown(s)

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Free Fall 2 dim Projectile Motion

• Typical problem Find range with v012m/s at 30o
  from horizontal

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UCM

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ucm

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UCM

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UCM- av2/r arw2

• Q1 Preliminary question When you close your
  eyes, which of the following do you feel?
• Position
• Velocity
• Acceleration
• Q1 Youre on a merry-go-round going around to
  quickly for the five course lunch you just had.
  In order to minimize the effect you should move
  toward
• A. the center
• B. the outside or,
• C. stay put

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SAMPLE PROBLEM CAR AND SMELLY TRUCK

• Good for drawing and equation set up. A car is
  travelling at 26m/s, 250m behind a truck
  travelling at 18 m/s. A truck is coming upon a
  tunnel 400m in front of it when the car decides
  to try and pass it before the tunnel. What is
  the minimum acceleration required by the car to
  pass the truck. Whats the velocity of the car as
  it passes the truck?

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SAMPLE PROBLEM SPECIAL PROJECTILE MOTION

• (Good for dwg, set-up and projectile) A rescue
  plane is travelling at 110m/s at an altitude of
  150m to drop a package to a shipwrecked chemist
  on an extremely tiny island. Luckily the pilot
  is a physicist and knows at what angle she should
  sight the poor chemist when she drops the
  package, in order for it to land at the foot of
  the chemist.

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