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Your roommate is working on his bicycle and has the bike upside down. He spins the 54.0 cm diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. A. What is the pebble's speed? B. What is the period of the pebble stone?

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Answer:

If the diameter is 54cm, then the radius is half that, the radius is:

r = 54cm/2 = 27cm

Then the perimeter of the wheel is p = 2*pi*27cm

this would mean that the pebble travels the distance:

d = 3*2*pi*27cm in one second.

Then the velocity of the pebble is:

speed = 3*2*3.1416*27cm/s = 509cm/s

Now, we know that the pebble does 3 cycles in a second, so does each cycle in 1/3 seconds, so the period would be the time that it needs to do one cycle, that we already find that is equal to 1/3 seconds.