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Welcome back to Physics 211. Today’s agenda: Review Vectors Vector components. ConcepTest 8. You are throwing a ball…. Acceleration of ball rolling on incline. Acceleration is not zero at top. velocity. time. Vectors. are used to denote quantities that have magnitude and direction

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Welcome back to physics 211

Welcome back to Physics 211

Today’s agenda:

Review

Vectors

Vector components


Conceptest 8

ConcepTest 8

You are throwing a ball…



Acceleration is not zero at top
Acceleration is not zero at top

velocity

time


Vectors
Vectors

  • are used to denote quantities that have magnitude and direction

  • can be added and subtracted

  • can be multiplied or divided by a number

  • can be manipulated graphically (i.e., by drawing them) or algebraically (usually by considering components)


Examples
Examples

  • Numbers: temperature, pressure, volume ….

  • Vectors: position, velocity, force


Adding vectors

Adding vectors

To add vector B to vector A:

Draw vector A.

Draw vector B with its tail starting from the tip of A.

The sum vector A+B is the vector drawn from the tail of vector A to the tip of vector B.



Find the vector b a
Find the vector “B – A”

1.

2.

3.

4.


Two unknown vectors A and B are added.

The magnitude of the sum vector “A + B” (i.e., the quantity |A + B|)

1. is at least as great as |A| (i.e., the magnitude of A).

2. is at most as great as |A| + |B| (i.e., the magnitudes of A and B added).

3. must be equal to |A| + |B|.

4. can be greater than |A| + |B|.


Projection of a vector

Projection of a vector

Component of a vector

“How much a vector acts along some arbitrary direction”

Projection onto one of the coordinate axes (x, y, z)


Components
Components

y

A=Ax+Ay

A

A=axi+ayj

Ay

q

i unit vector in x direction

x

Ax

j unit vector in y direction

ax,ay components of vector A

Projection of A along coordinate axes


More components
More components

  • Note:

    ax=|A|cosq, ay=|A|sinq

  • |A|2=ax2+ay2


Why components useful
Why components useful ?

  • Addition: just add components

    if C=A+B

    cx=ax+bx; cy=ay+by

  • Magnitude |A|2=ax2+ay2

  • Direction tanq=ay/ax



A bird is flying along a straight line in a direction somewhere East of North. After the bird has flown a distance of 2.5 miles, it is 2 miles North of where it started.

How far to the East is it from its starting point?

1. 0 miles

2. 0.5 miles

3. 1.0 mile

4. 1.5 miles


2d motion
2D Motion somewhere East of North. After the bird has flown a distance of 2.5 miles, it is 2 miles North of where it started.

Note:

component of position vector

along x direction is the x coordinate!

s – vector position

s=xi+yj


Describing motion with vectors somewhere East of North. After the bird has flown a distance of 2.5 miles, it is 2 miles North of where it started.

  • Positions and displacements

    s,Ds = sfinal - sinitial

  • Velocities and changes in velocity:

    vave= ––––,vinst= lim ––––,

    Dv = vfinal - vinitial

  • Acceleration: aave= ––––,ainst= lim ––––,

Dt0

Dt0


Quick quiz 3 3 from serway beichner physics
Quick Quiz 3.3 somewhere East of North. After the bird has flown a distance of 2.5 miles, it is 2 miles North of where it started.(from: Serway/Beichner, Physics)

Can any component of a vector ever be greater than the magnitude of the vector?

1. Yes

2. No

3. Not sure


Quick quiz 3 4 from serway beichner physics
Quick Quiz 3.4 somewhere East of North. After the bird has flown a distance of 2.5 miles, it is 2 miles North of where it started.(from: Serway/Beichner, Physics)

If one component of a vector is not zero, can the magnitude of the vector be zero?

1. Yes

2. No

3. Not sure


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