Question

A carousel at the local carnival rotates once every 45 seconds.

Answer 1

Answer:

We know that the carousel does a complete rotation in 45 seconds.

Then the frequency of this carousel will be f =  1/45 seconds.

And the angular frequency will be 2*pi times the frequency, then we have:

angular frequency = w = 2*3.14*(1/45s) = 0.1396 s^-1

Now, the linear speed of an object that rotates with a radius R, and an angular frequency W is:

S = R*W

then:

a) in this case the radius is 2.75m, then the linear speed is:

S = 2.75m*0.1396 s^-1 = 0.3839 m/s

b) in this case the radius is 1.75m, then the linear speed here is:

S = 1.75m*0.1396 s^-1 = 0.2443 m/s