M1 OCR: Vectors, Forces and Friction

Topic 1 of the OCR M1 A Level

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  • Created on: 28-05-12 09:26
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1. Vectors, Forces and Friction
Vectors have magnitude and direction
To find the resultant force, line up all the forces
tip to tail and connect them up
Use the sine / cosine rules and rules about
angles and parallel lines
Remember for bearings go clockwise
Unit Vectors
o Vector of magnitude 1
o Make components of the vector: i and j
o X direction: i
o Y direction: j
o E.g. if you have a vector 16i + 12j with a
magnitude 20, the unit vector is 1/20 (16i + 12j)
or 0.8i + 0.6j
When adding vectors: just add the i and j
o E.g. A = 3i + 2j plus B = 5i ­ 6j
o A + B = 8i ­ 4j
o To find the resultant force of A + B, make a
Pythagorean triangle
Making components
o X axis: v cos
o Y axis: v sin
o V = v cos i + v sin j
If a force is applied vertically it doesn't apply
at all horizontally and vice versa
If a force is applied at an angle then it is
applied vertically and horizontally
o Vertical component: F sin
o Horizontal component: F cos
On an inclined plane, resolve parallel and
perpendicular to the slope
o Weight acts straight downwards

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