Question

Suppose the second hand on a clock is 3 inches long. Find the linear velocity of the tip of the second hand.

Answer 1

what is the circumference of a circle with radius 3?

Answer 2

6pi or 18.8

Answer 3

let's stick with 6pi since it's exact

Answer 4

okay

Answer 5

by definition, the second hand moves around the full circle in 60 seconds (assuming the clock is working properly)

so it covers 6pi inches in 60 seconds

we can form this fraction

\[\Large \frac{6 \pi \ \text{ inches}}{60 \ \text{ seconds}}\]

to represent the speed of the tip of the second hand

Answer 6

Ohh!

Answer 7

now simply reduce that fraction

\[\Large \frac{6 \pi \ \text{ inches}}{60 \ \text{ seconds}} = \frac{\pi \ \text{ inches}}{10 \ \text{ seconds}}\]

Answer 8

the exact linear speed is pi/10 inches per second

approx that is 0.31415926535898 inches per second

since
pi/10 = 0.31415926535898

Answer 9

Thank you so much, I was so confused at first when I read this :)

Answer 10

no problem

Answer 11

:)