# Thread: linear speed and centripetal acceleration

1. ## linear speed and centripetal acceleration

The front and rear sprockets on a bicycle have radii of 9.00 and 5.10 cm, respectively. The angular speed of the front sprocket is 6.00 rad/s. Determine the following.
(a) The linear speed of the chain as it moves between the sprockets.
cm/s

(b) The centripetal acceleration of the chain as it passes around the rear sprocket.
cm/s2

i think the formula is something like: sqrt(r^2 * w^4 + r^2((w-w0)/t)^2)

however, there are two radius' ?

also, not sure how to compute the speed.

2. Originally Posted by rcmango
The front and rear sprockets on a bicycle have radii of 9.00 and 5.10 cm, respectively. The angular speed of the front sprocket is 6.00 rad/s. Determine the following.
(a) The linear speed of the chain as it moves between the sprockets.
cm/s
The chain can only move at one linear speed over either sprocket. So we know the radius and angular speed of the front sprocket, thus
$v = r_f \omega _f$
(where the subscript "f" repesents the front sprocket.)

Originally Posted by rcmango
(b) The centripetal acceleration of the chain as it passes around the rear sprocket.
cm/s2
We now know the linear speed of the chain so we can calculate the angular speed of the rear sprocket:
$v = r_r \omega _r$

$\omega _r = \frac{v}{r_r}$

Now we can calculate the centripetal acceleration of the chain as it goes around the rear sprocket:
$a_c = r \omega ^2$

Hint: Stick to the basics when problem solving. I don't even recognize that formula you posted.

-Dan