Question

If a 50 tooth sprocket turns at a speed of 20 rpm how many rpm will a 30 tooth sprocket turn

Answer 1

When two sprockets are in contact with each other then at the contact of sprockets the tangential velocity and tangential acceleration of the sprockets must be same.

Now we can say that tangential velocity is given as

v = Rw

here we know that

$w = 2\pi f$

also we can say

$2\pi R = N*x$

x = width of each sprocket

So tangential speed is given as

$v = \frac{N*x}{2\pi} * 2\pi f$

now since tangential speed of two sprockets are same

$N_1*x*f_1 = N_2*x*f_2$

given that

$N_1$ = 50

$f_1$ = 20 rpm

$N_2$ = 30

now from above equation

$50*20 = f_2 * 30$

$f_2 = \frac{100}{3}$ rpm