Saturday

January 24, 2015

January 24, 2015

Posted by **Joe** on Sunday, November 18, 2007 at 5:53pm.

a. second hand which is 30 millimeters.

b. minute hand which is 27 millimeters long.

c. hour hand which is 18 millimeters long.

Please tell me how you got the answer. Thanks!

- PreCalc -
**Michael**, Sunday, November 18, 2007 at 6:04pmLinear velocity equals angular velocity (in radians) multiplied by radius.

Let's start by calculating angular velocity. Angular velocity is a measure of the angular displacement per unit time. (The angular velocity of a particle traveling on a circular path is the ratio of the angle traversed to the amount of time it takes to traverse that angle.) w = angle/time

From what you've told me, I'm going to assume we are rotating one hour, which is an entire circle. That is 360 degrees, or 2(pi) radians. Note that one hour is 3600 seconds, and the length of each hand is the radius.

a. w = angle/time = 2(pi) / 3600 = (pi)/1800.

Linear velocity is that times radius. (pi/1800)*30 = 30(pi)/1800 = pi/60 mm/sec

Do a similar process for b and c, and I'll critique your thinking. If you have any questions, let me know.

- PreCalc -
**Lincoln**, Sunday, November 18, 2007 at 6:08pmWell I looked in the back of my book, and for a, the answer is shown as 3.1 mm/s.

- PreCalc -
- PreCalc -
**Michael**, Sunday, November 18, 2007 at 6:10pmWell, my assumption that each hand is rotating one hour may be incorrect. How far is each hand rotating?

- PreCalc -
**Reiny**, Sunday, November 18, 2007 at 10:53pma) for the second hand..

it rotates 2pi rad/min

=2pi/60 rad/sec

= pi/30 rad/sec and it is 30 mm long

so the linear velocity = (pi/30)(30 mm/sec

= pi mm/sec

= 3.14159 mm/sec (you book had 3.1)

b) for the minute hand

it rotates 2pi radians per hour

= 2pi/3600 rad/sec

so linear vel. = pi/1800)(27) mm/sec

= appr .048 mm/sec

c) the hour hand rotates 2pi radians each 12 hours

so angular vel. = 2pi/(43200) rad/sec

linear vel. = 18(2pi/43200) mm/sec

= appr. .00262 mm/sec

**Answer this Question**

**Related Questions**

Algebra 2 - What is the angular speed in radians per second of the hour hand of ...

physics - The minute hand of a large clock is 0.50 m long. (A) Calculate its ...

physics - A clock has a second hand whose tip rubs against the inside of the ...

Physics - A clock has a second hand whose tip rubs against the inside of the ...

physics (centripetal acceleration) - The second hand and the minute hand on one...

Trig - Find the speed in both radians per second and degrees per second for the ...

Math (PreCalculus) - The second hand of a clock is 4 inches long. Describe the ...

Physics- Mechanics - The speed of the tip of the minute hand on a town clock is ...

Trig - Linear and angular speed Find w for each of the following: 1. the minute ...

Physics - Find the angular velocity of a clock's second hand and the linear ...