Thread: 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.

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

(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:




Now we can calculate the centripetal acceleration of the chain as it goes around the rear sprocket:


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

-Dan