Nonuniform Circular Motion

j / 1. Moving in a circle while speeding up. 2. Uniform circular motion. 3. Slowing down.

What about nonuniform circular motion? Although so far we have been discussing components of vectors along fixed x and y axes, it now becomes convenient to discuss components of the acceleration vector along the radial line (in-out) and the tangential line (along the direction of motion). For nonuniform circular motion, the radial component of the acceleration obeys the same equation as for uniform circular motion,

a_r = |v|²/r ,

but the acceleration vector also has a tangential component,

a_t = slope of the graph of |v| versus t .

The latter quantity has a simple interpretation. If you are going around a curve in your car, and the speedometer needle is moving, the tangential component of the acceleration vector is simply what you would have thought the acceleration was if you saw the speedometer and didn't know you were going around a curve.

Slow down before a turn, not during it.

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