# Math Help - help me on solving this problem please

1. ## help me on solving this problem please

hi guys ! i don't wanna disturbe you but i truly need to solve this problem:
An object is travelling around a circle with a radius of 10 cm. If in 20 seconds a central angle of 1/3 radian is swept out, what is the linear speed of the object?

2. Originally Posted by alessandromangione
hi guys ! i don't wanna disturbe you but i truly need to solve this problem:
An object is travelling around a circle with a radius of 10 cm. If in 20 seconds a central angle of 1/3 radian is swept out, what is the linear speed of the object?
If the circle has radius of 10cm, then

$C = 2\pi \cdot 10\,\textrm{cm}$

$C = 20 \pi \,\textrm{cm}$.

It has travelled $\frac{1}{3}$ of a radian.

Since there are $2\pi$ radians on the circumference, that means 1 radian $= \frac{C}{2\pi}$.

Therefore $\frac{1}{3}\,\textrm{radian} = \frac{C}{6\pi}$.

Since the circumference was $20 \pi \,\textrm{cm}$

$\frac{1}{3}\,\textrm{radian} = \frac{20\pi\,\textrm{cm}}{6\pi}$

$\frac{1}{3}\,\textrm{radian} = \frac{10}{3}\,\textrm{cm}$.

Since it travels this far in 20 seconds, or $\frac{1}{3}\,\textrm{min}$, this means that the speed is

$\frac{10}{3}\,\textrm{cm}$ per $\frac{1}{3}\,\textrm{min}$

or

$10\,\textrm{cm}\, / \, \textrm{min}$.

3. first of all thank you very much for answwering.
But i tried to do it in another way and the result is different.
since the angular speed is obtained by 1/3 : 20 seconds ( angle divided per time) i got 1 /60 . Then i applied the formula v= radius angular speed , so v= 1/60 multiplied per 10 i got 1/6...the teacer told me to use the formulas above written but the result is different from yours...where did i mistake?

4. Originally Posted by alessandromangione
first of all thank you very much for answwering.
But i tried to do it in another way and the result is different.
since the angular speed is obtained by 1/3 : 20 seconds ( angle divided per time) i got 1 /60 . Then i applied the formula v= radius angular speed , so v= 1/60 multiplied per 10 i got 1/6...the teacer told me to use the formulas above written but the result is different from yours...where did i mistake?
Your result is the speed in cm/s. Multiply by 60 s/min to get the speed in cm/min.

You'll get the same result as ProveIt.

5. Originally Posted by alessandromangione
first of all thank you very much for answwering.
But i tried to do it in another way and the result is different.
since the angular speed is obtained by 1/3 : 20 seconds ( angle divided per time) i got 1 /60 . Then i applied the formula v= radius angular speed , so v= 1/60 multiplied per 10 i got 1/6...the teacer told me to use the formulas above written but the result is different from yours...where did i mistake?
Speed is not the ratio of angle to time. It's the ratio of distance to time.

So you need to work out the distance travelled.

6. Originally Posted by earboth
...
so..1/3 x 2 greek pi ( i don't know how to put the symbol sorry ) divided by 20 and i get 2 greek pi/ 60 then i multiplied this per 10 and i get 2 greek pi / 6...the result isn't 10 cm/min i'm confused.......can you explain me the procedure using this way?

7. Did you read my post?

It has not travelled $\frac{1}{3}$ of $2\pi$.

It has travelled $\frac{1}{3}$ of a RADIAN.

Like I said, $2\pi^r = C$, so $1^r = \frac{C}{2\pi}$.

So it has travelled $\frac{1}{3}^r = \frac{C}{6\pi}$.

8. Originally Posted by alessandromangione
so..1/3 x 2 greek pi ( i don't know how to put the symbol sorry ) divided by 20 and i get 2 greek pi/ 60 then i multiplied this per 10 and i get 2 greek pi / 6...the result isn't 10 cm/min i'm confused.......can you explain me the procedure using this way?
I've made a very silly mistake in my previous post. It's already "repaired"!

9. Originally Posted by earboth
I've made a very silly mistake in my previous post. It's already "repaired"!
ok thanks anyway!