chapter 3 (continued) vectors in physics

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Chapter 3 (continued)

Vectors in Physics


Review: The Components of a VectorCan resolve vector into perpendicular components using a two-dimensional coordinate system:


3-2 The Components of a VectorLength, angle, and components can be calculated from each other using trigonometry:Ax = A cos θ, Ay = A sin θA: magnitudeOr:A = (Ax

2 + Ay2)1/2

θ = tan-1 (Ay / Ax)


Express a vector in terms of unit vectors: yAxAA yx ˆˆ +=


Adding and Subtracting Vectors

Formula using unit vectors

yAxAA yx ˆˆ +=

yBxBB yx ˆˆ +=

yBAxBABA yyxx ˆ)(ˆ)( +++=+


3-5 Position, Displacement, Velocity, and Acceleration Vectors

Position vector points from the origin to the location in question.

The displacement vectorpoints from the original position to the final position.

fr

rΔ



Average velocity vector:

(3-3)

So is in the same

direction as .avv

rΔ


Key: find the displacement vector

Ask: draw those vectors in xy plane in blackboard?



Instantaneous velocity vector is tangent to the path:



Average acceleration vector is in the direction of the change in velocity:


Ask: can anyone sketch the vector In blackboard?


Find the average acceleration for the time interval of 10.0 s.


Drawn these vectors in x-y plane


3-6 Relative MotionThe speed of the passenger with respect to the ground depends on the relative directions of the passenger’s and train’s speeds:


3-6 Relative Motion

This also works in two dimensions:


a train


Example 3-2 Crossing a riverYou are riding in a boat whose speed relative to the water is 6.1 m/s. The boat points at an angle of 25o upstream on a river flowing at 1.4 m/s. (a) what is your velocity relative to the ground?

(b) Suppose the speed of the boat relative to the water remains the same, but the direction in which it points is changed. What angle is required for the boat to go straight across the river?


Summary of Chapter 3

• Scalar: number, with appropriate units

• Vector: quantity with magnitude and direction

• Vector components: Ax = A cos θ, By = B sin θ

• Magnitude: A = (Ax2 + Ay

2)1/2

• Direction: θ = tan-1 (Ay / Ax)

• Graphical vector addition: Place tail of second at head of first; sum points from tail of first to head of last


• Component method: add components of individual vectors, then find magnitude and direction• Unit vectors are dimensionless and of unit length• Position vector points from origin to location• Displacement vector points from original position to final position• Velocity vector points in direction of motion• Acceleration vector points in direction of change of motion• Relative motion:

Summary of Chapter 3

13 12 23v = v + v

chapter 3 (continued) vectors in physics

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