Circular Motion Video Lessons

Concept

# Problem: A rotating fan completes 1200 revolutions every minute. Consider a point on the tip of a blade, at a radius of 0.14 m.(a) Through what distance does the point move in one revolution?(b) What is the speed of the point?(c) What is the magnitude of its acceleration?(d) What is the period of the motion?

###### FREE Expert Solution

We need to know some quick formula relating to our problem.

The distance covered around a circle is circumference given by:

$\overline{){\mathbf{Distance}}{\mathbf{=}}{\mathbf{2}}{\mathbf{\pi r}}}$, where r is the radius.

Speed,

$\overline{){\mathbf{v}}{\mathbf{=}}{\mathbf{r}}{\mathbf{\omega }}}$, where ω is the angular velocity.

Centripetal acceleration:

$\overline{){{\mathbf{a}}}_{{\mathbf{c}}}{\mathbf{=}}\frac{{\mathbf{v}}^{\mathbf{2}}}{\mathbf{r}}{\mathbf{=}}{\mathbf{r}}{{\mathbf{\omega }}}^{{\mathbf{2}}}}$

Time period, T:

$\overline{){\mathbf{T}}{\mathbf{=}}\frac{\mathbf{D}\mathbf{i}\mathbf{s}\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{c}\mathbf{e}}{\mathbf{v}}}$

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###### Problem Details

A rotating fan completes 1200 revolutions every minute. Consider a point on the tip of a blade, at a radius of 0.14 m.
(a) Through what distance does the point move in one revolution?
(b) What is the speed of the point?
(c) What is the magnitude of its acceleration?
(d) What is the period of the motion?