M1 Maths Mechanics - Revision Notes/Posters

Printable PDF. Covers the entire Maths & Mechanics course from the beginning, ideal for notes (for revision) and as a series of posters for blu-tacking to the wall a few weeks before your exams.

From the EDEXCEL M1 specification.

Thank you, and I hope it's of use to you.

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  • Created by: Lawrence
  • Created on: 02-04-10 22:17
Preview of M1 Maths Mechanics - Revision Notes/Posters

First 52 words of the document:

Common Equations of Motion (M1.3)
Equations without
DISPLACEMENT v=u+at
Equations without
FINAL VELOCITY s=ut+½at 2
Equations without
INITIAL VELOCITY s=vt-½at 2
Equations without
TIME
2 2
v = u + 2as
Equations without
ACCELERATION s = ½ (u + v) t

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Page 2

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Momentum and Impulse (M1.4)
Momentum
Velocity and Mass =mv
Impulse
Combining Momentum =mv­mu
For collisions.…read more

Page 3

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Vectors in Mechanics ­ M1.2
Magnitude and direction of a vector.
Vectors can be considered as triangles.
You use SIN, COS and TAN to RESOLVE vectors
to multiple dimensions, just as you'd use them for
unknown lengths of sides.
You can use the rules of Pythagoras to determine
the magnitude of the RESULTANT.…read more

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Page 5

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Kinematics of a Particle ­ M1.3
Motion in a straight line with constant acceleration.
The gradient of a displacement-time
graph is the VELOCITY.
The gradient of a velocity-time graph
is the ACCELERATION.
The area under a velocity-time graph
is the DISPLACEMENT.
Example graph from Question:
Knowledge and use of formulae
for constant acceleration will
be required.
(Refer to Common Equations of Motion M1.3.…read more

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Newton's Laws (M1.4)
Think 'frame of reference'.
Newton's First Law.
An object will not change its Newton's Second Law.
velocity until an unbalanced
force acts upon it.
f = ma
Newton's Third Law.
Every action has an equal and
opposite 're-action'.
Force (in Newtons) equals
mass times acceleration.
Image by 'Benjamin Crowell' of Wikipedia.…read more

Page 7

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Single-dimension Dynamics of a Particle (M1.4)
You should know:
· Newton's Three Laws.
· 1 Newton (mass times acceleration) is 1 kg m s -2.
· Impulse, Momentum and applications (e.g. collisions).
· Co-efficient of Friction:
On a rough surface, with Co-efficient of Friction
0.7, the Friction can be determined with the
F=R
equation Friction = 0.7 * Reaction.
The Co-efficient of Friction, multiplied
The object is not moving upwards, so Reaction is
equal to Weight.
by the Reaction force equals the
R
Friction.…read more

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Statics of a Particle (M1.5)
Sometimes it can be quicker to
Friction
FR
RESOLVE forces with a different
frame of reference.
- Friction acts opposite the For instance, perpendicular to a
plane, so less forces have to be
resultant force. resolved.
In practice, in
- Friction is always less than or equlibrium, Friction
may not be EQUAL to
equal to the resultant force.
c.o.fr. times reaction.
If this is the case, dimensions x
and y will both resolve to 0.…read more

Page 9

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Moments (M1.5)
In the first diagram, the moment of force 'F' about
10 N point 'A' is F * d.
Fixed about point A The second diagram represents a couple. Across
and in equlibrium. any direction, it resolves to nothing, so the object
would rotate but not move.
A
sm
10 N
Moment = E*s
For some problems, you must also
EN
RESOLVE HORIZONTALLY,
and for some just as moments.
M=F*s Moments in each direction
(clockwise and anti-clockwise) are
equal while in equilibrium.…read more

Page 10

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Mechanical Models and Terms ­ M1.1
A single object without specific Inextensible Cannot change in length.
Particle
structure or internal motion.
Smooth/Rough No friction/subject to friction.
Lamina Thin plate or layer.
Pulley Adjusts direction of motion
Rigid Body Size and shape are fixed definitely.
Bead Particle confined to wire.
Rod Single-dimension lamina.
Inextensible string to which beads
Wire
Light No conceivable mass. are confined.
Uniform Of a consistent density/structure. Peg To fix within a certain range.…read more

Comments

daviesg

Really well presented poster showing Newtons laws of motion.  excellent for revision.

ShelleyK

Awesome really clear and helpful

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