Physics / Unit 4: Circular Motion and Gravity
4.1 Uniform Circular Motion
Notes
Uniform circular motion is motion in a circle at constant speed. The velocity keeps changing direction, so the object is accelerating.
- Period $T$: time for one full circle (s). Frequency $\displaystyle f = \frac{1}{T}$: circles per second (Hz).
- Speed: $\displaystyle v = \frac{2\pi r}{T}$ (circumference divided by period).
- The velocity at any instant is tangent to the circle.
- Example: a ball on a 2 m string circles once every 4 s. $\displaystyle v = \frac{2\pi(2)}{4} \approx 3.14 \text{ m/s}$.
Practice
A merry-go-round makes 1 full turn every 5 s. What is its frequency?
$\displaystyle f = \frac{1}{T} = \frac{1}{5} = 0.2 \text{ Hz}$.
A runner circles a track of radius 50 m in 100 s. What is her speed?
$\displaystyle v = \frac{2\pi(50)}{100} \approx 3.14 \text{ m/s}$.
A stone is whirled in a horizontal circle and the string breaks. Which way does the stone move just after?
With no inward force, the stone moves in a straight line along its velocity, which was tangent to the circle.
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