Phys 270- 1: Units, Physical Quantities, And Vectors

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Theory:

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an explanation of natural phenomena based on observation and accepted fundamental principles

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"acceleration of a falling body is independent of its weight" who was the first to think of this idea?

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galileo galilei

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Physics:

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the process by which we arrive at general principles that describe how the physical universe behaves.

- the study of all aspects of the universe.

- about understanding how everything works

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range of validity:

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it applies to a range of how valid a theory is.

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Problem solving strategy 1.1: solving physics problems

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Model:

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a simplified version of a physical system that would be too complicated to analyze in full detail.

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Physical quantity:

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any # that is used to describe a physical phenomenon quantitatively.

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time:

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based on an atomic clock which uses the energy difference between the two lowest energy states of the cesium atom

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second (s):

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the time required for 9,192,631,700 cycles of cesium atom's microwave radiation

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meters (m):

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the distance that light travels in a vaccum in 1/299,792,458 sec.

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kilograms (kg):

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the mass of a particular cylinder of platinum-iridium alloy kept at the international bureau of weights and measures.

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formula for distance:

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d = vt

v= velocity
t= time

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Problem-solving strategy 1.2: unit conversions:

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uncertainty: (aka: error):

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b/c it indicates the max. difference there is likely to be between the measured value and the true value.

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accuracy:

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how close it is likely to be the true value.

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Using significant figures:

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velocity:

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the speed combined with its direction of motion

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force:

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a push/pull exerted on a body

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scalar quantity:

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a single number

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vector quantity:

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has magnitude ("how much" or "how big") & a direction in space.

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Displacement:

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- simply a change in position of a point.

- is a vector quantity because we must state no only how far the particle moves, but also in what direction it is moving.

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What does negative of a vector mean?

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a vector having the same magnitude as the original vector but the opposite direction "antiparallel"

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Components of a vector:

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are just numbers, not vectors themselves.

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definition of vector components from that of the trig. functions:

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Finding the magnitude of a vector:

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Finding the direction of a vector:

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Unit Vector:

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- a vector that has a magnitude of 1 with no units.

- only purpose is to point... to describe a direction in space.

- (^) "hat/caret" symbol for a unit vector to distinguish it from ordinary vectors whose magnitude may/ maynot = 1

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Unit Vector:

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- a vector that has a magnitude of 1 with no units.

- only purpose is to point... to describe a direction in space.

- (^) "hat/caret" symbol for a unit vector to distinguish it from ordinary vectors whose magnitude may/ maynot = 1

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Scalar product (dot product):

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- draw the two vectors with their tails at the same point.

- angle between their direction ranges from 0 - 180.

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definition of the scalar (dot) product:

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The scalar product of two parallel vectors is always equal to?

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0

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The scalar (dot) product in terms of components:

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the scalar product of two vectors is the sum of the products of their respective components.

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Vector product (cross product):

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- denoted by vector A x vector B

- draw the two vectors with their tails at the same point.

- a vector quantity with a direction parallel to this plane (parallel to both vector A and B).

- the angle from vector A to vector B and take it to be the smaller of the two possible angles from 0 - 180 then sin of the angle is greater than or equal to 0 and C is never negative.

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The vector product of two parallel or antiparallel vectors is always = ?

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0

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The vector product of any vector with itself is ?

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0

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cross product (vector product) not commutative..

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the right hand rule:

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vector product can also be expressed in determinant form as:

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law of nature:

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represents our best understanding of how nature behaves given certain limiting assumptions.

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Summary:

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