Finding speed in inches/mins?

Question

The minute hand of the tower clock is 8.0 feet long. Assuming the hand moves at a constant angular velocity, find the speed of the tip of the hand in inches/mins. Do the same for an hour hand of 6.00 feet?

Answer 3.2 pi in/min

Equations to use?

Answer 1

First of all you have to get the distance that the tip moves.
The tip describes a circle with radius equal to the length of the hand.

so, the minute hand describes a circle with radius = 8 feet.

The circumferance (or length of sweep) is found with equation.

c=pi*dia or c=pi*2*r

at r=8 feet, r=96 inches (you were asked to get the tip speed in inches/mins)

c=pi*2*96 = 192*pi inches

thats the distance, now how long does it take to go that distance?
how long does it take for the minute hand to sweep out a whole circle?
One hour of course (60 mins).

so, the tip goes 192*pi inches in 60 minutes
or 192/60= 3.2pi inches/min

The hour hand problem is the same except that it is only 6 feet long so the circle is c=2*6*12pi inches and, it takes the hour hand a lot longer to sweep the circel (12 hours or 720 minutes).

Got it?
Go wild.