MHB Angular and Linear Speed of a Point

AI Thread Summary
The discussion focuses on calculating angular and linear speed, specifically addressing the relationship between angle and arc length. The angle generated is confirmed to be \( \frac{2\pi}{3} \) radians, derived from the equation \( \theta = \omega t \). The linear distance is calculated using the formula \( s = \theta r \), resulting in \( 40\pi \) cm for a radius of 60 cm. The linear speed is also discussed, yielding \( \frac{5\pi \text{ cm}}{s} \). Overall, the calculations are confirmed to be correct.
karush
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my ? on (i) is since it is asking for an angle and not a arc length
then the angle generated would be just

$$\displaystyle 8\frac{\pi}{12}=\frac{2\pi}{3}$$

or not?
 
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Yes, that's right, although you might want to get in the habit of carrying the units as a means of making sure your result is dimensionally correct:

$$\theta=\omega t=\frac{\pi}{12}\frac{\text{rad}}{\text{s}} \cdot8\text{s}=\frac{2\pi}{3}\text{ rad}$$
 
so (ii) would be just $\text {s}=\theta\text{ r}$

$\displaystyle\frac{2\pi}{3}\text{rad}\cdot60\text { cm}=40\ \pi\text { cm}$

and (iii) would be

$\displaystyle \frac{5\pi\text { cm}}{s}$
 
Last edited:
karush said:
so (ii) would be just $\text {s}=\theta\text{ r}$

$\displaystyle\frac{2\pi}{3}\text{rad}\cdot60\text { cm}=40\ \pi\text { cm}$

and (iii) would be

$\displaystyle \frac{5\pi\text { cm}}{s}$

Yes, those are correct.(Sun)
 
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