Post on 19-Oct-2021
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Chapter 3 (continued)
Vectors in Physics
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Review: The Components of a VectorCan resolve vector into perpendicular components using a two-dimensional coordinate system:
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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)
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Express a vector in terms of unit vectors: yAxAA yx ˆˆ +=
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Adding and Subtracting Vectors
Formula using unit vectors
yAxAA yx ˆˆ +=
yBxBB yx ˆˆ +=
yBAxBABA yyxx ˆ)(ˆ)( +++=+
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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
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3-5 Position, Displacement, Velocity, and Acceleration Vectors
Average velocity vector:
(3-3)
So is in the same
direction as .avv
rΔ
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Key: find the displacement vector
Ask: draw those vectors in xy plane in blackboard?
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3-5 Position, Displacement, Velocity, and Acceleration Vectors
Instantaneous velocity vector is tangent to the path:
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3-5 Position, Displacement, Velocity, and Acceleration Vectors
Average acceleration vector is in the direction of the change in velocity:
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Copyright © 2010 Pearson Education, Inc.
Ask: can anyone sketch the vector In blackboard?
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Find the average acceleration for the time interval of 10.0 s.
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Drawn these vectors in x-y plane
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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:
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3-6 Relative Motion
This also works in two dimensions:
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a train
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a train
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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?
Copyright © 2010 Pearson Education, Inc.
Copyright © 2010 Pearson Education, Inc.
Copyright © 2010 Pearson Education, Inc.
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
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• 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