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•Describe motion in terms of frame of reference•Express scalar and vector quantities•Understand the relationship between scalar and vector quantities
Motion• One-dimensional motion is the simplest form
of motion– A change in position– Motion that takes place in one direction- X or Y direction but not simultaneously
Motion takes place over time and depends upon the frame of reference•Frame of reference – a coordinate
system for specifying the precise
location of objects in space; a point that is
used to compare another objects motion
ScalarA SCALAR is ANY quantity in
physics that has MAGNITUDE, but NOT a direction associated with it; it has nothing to do with spacial direction
Magnitude – A numerical value with units.
Scalar Example
Magnitude
Speed 20 m/s
Distance 10 m
Age 15 years
Heat 1000 calories
VectorA VECTOR is ANY quantity in
physics that has BOTH MAGNITUDE and DIRECTION.
Vector Magnitude & Direction
Velocity 20 m/s, N
Acceleration 10 m/s/s, E
Force 5 N, West
Faxv,,,
Vectors are typically illustrated by drawing an ARROW above the symbol. The arrow is used to convey direction and magnitude.
More about Vectors
• A vector is represented on paper by an arrow1. the length represents magnitude2. the arrow faces the direction of motion
Vectors can be added graphically
• Resultant – answer found by adding vectors
Vectors can be added graphically
The goal is to draw a mini version of the vectors to give you an accurate picture of the magnitude and direction. To do so, you must:
1. Pick a scale to represent the vectors. Make it simple yet appropriate.
2. Draw the tip of the vector as an arrow pointing in the appropriate direction.
3. Use a ruler & protractor to draw arrows for accuracy. The angle is always measured from the horizontal or vertical where the motion started.
• Vectors can be moved parallel to themselves in a diagram
• Vectors can be added in any order
• To subtract a vector, add its opposite
Vectors can be added graphically
Determining resultant magnitude• If the movement is in
straight lines that form a right triangle, Use the Pythagorean theorem to find the magnitude of the resultant
• Pythagorean Theorem for right triangles
d2 = x2 + y2
(Length of hypotenuse)2 = (length of one leg)2 + (length of the other leg)2
Determining resultant magnitude
Determining resultant magnitude
• To completely describe the resultant you also need to find the direction also
• When the resultant forms a right triangle, use the tangent function to find the angle (θ) of the resultant
Determining resultant direction
DETERMINING DIRECTION
B A
CD
N of E
N of W
S of W
S of E
• The angle (θ) of the resultant is the direction of the resultant
Determining resultant direction
Determining resultant direction
To find just the angle, use the inverse of the tangent function
• Remember when you solve for the displacement you are looking for the magnitude (d) and the direction (Θ with descriptor)
Kangaroos can easily jump as far as 8.0m. If a kangaroo makes five such jumps westward, how many jumps must it take northward to have a northwest displacement with a magnitude of 68m? What is the angle of the resultant displacement with respect to the north?
The emperor penguin is the best diver among birds: the record dive is 483m. Suppose an emperor penguin dives vertically to a depth of 483m and then swims horizontally a distance of 225m to the right. What angle would the vector of the resultant displacement make with the water’s surface? What is the magnitude of the penguin’s resultant displacement?