MECHANICS

SUMMARY

Vectors

A vector quantity needs a magnitude and direction in order to describe it fully.

The size of a vector quantity is called its magnitude.

On a page, a vector quantity is represented by an arrow drawn to scale.

To add two vector quantities join the vectors tip to tail in a chain.  The total is the vector that starts from the tail of the first in the chain and finishes at the tip of the last vector in the chain.

To subtract a vector from another, reverse the direction of the one being taken away and then add.

To multiply a vector by a number, maintain the direction of the original vector and then extend or reduce the length of the vector by a factor equal to the number.

A vector can be split into two components that add up to equal the original vector.

Many problems can be made simple by splitting a vector into two components at right angles to each other.  Vertical and horizontal for some situations.  Parallel to the slope and across the slope for hills.

When an object is on a slope, the component of the weight force down the incline equals the weight times the sine of the angle of the slope to the horizontal.

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When an object is on a slope, the component of the weight force across the incline equals the weight times the cosine of the angle of the slope to the horizontal.

When an object slides down a slope the normal reaction of the slope on the object is equal in size to the component of the weight force across the slope.

The velocity of an object relative to an observer equals the velocity of the object minus the velocity of the observer.

Dynamics

The tendency of an object to resist changes to its motion is called its inertia.

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