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Trigonometry Angular and Linear Speed of a Point

karush

Well-known member
Jan 31, 2012
2,771
View attachment 1429

my ? on (i) is since it is asking for an angle and not a arc length
then the angle generated would be just

\(\displaystyle \displaystyle 8\frac{\pi}{12}=\frac{2\pi}{3}\)

or not?
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
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:

\(\displaystyle \theta=\omega t=\frac{\pi}{12}\frac{\text{rad}}{\text{s}} \cdot8\text{s}=\frac{2\pi}{3}\text{ rad}\)
 

karush

Well-known member
Jan 31, 2012
2,771
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:

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
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)