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Page 1

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Vectors & Scalars
Vectors need both
magnitude and
direction to define
them.

Scalars only require
magnitude.

Page 2

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Vectors & Scalars
Vectors Scalars
Displacement Time

Velocity Energy

Acceleration Work

Force Distance

Moment Speed

Momentum Temperature

Page 3

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Equations
If you calculate a value
in Physics from an
equation (e.g. F=ma)
then the answer will
always be a scalar
value i.e. just the
magnitude of the
property calculated.

Page 4

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Limitations
Most of the time this
works fine, but we start
to run into trouble
when we consider
events happening in 2
or 3 dimensions.

Page 5

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Needing vectors
Things like forces acting
in several directions or
Flemming's Left Hand
Motor Rule. To fully
describe what is
happening in these
situations we need to
state directions; we
need vectors.

Page 6

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Problem
But if equations can
only deal with scalars,
then how can we use
equations with vectors?
Happily parallel vectors
have the same
direction, so we can
ignore it and treat them
like scalar values.

Page 7

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Adding vectors
Only parallel vectors
can be added together
(or subtracted)
algebraically. Non-
parallel vectors can
only be combined via a
scale diagram or if they
are...

Page 8

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Components
... resolved into
components.

The Components of a
vector are any two,
mutually perpendicular
vectors whose vector
sum is equal to the
original vector.

Page 9

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Components
Obviously it only makes
sense to resolve
different vectors into
components which form
parallel groups,
otherwise they cannot
be combined.

Page 10

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Components
Useless components:




Yes, these components are
mutually perpendicular, but
we still can't add or
subtract their magnitudes.

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