Angular Velocity of Analog Watch

[eoneil]

Homework Statement

Calculate the angular velocity of the second, minute, and hour hand of a watch.

Homework Equations

Assuming the watch is functioning normally, a second hand must travel the entire 360 degrees in 60 second. The formula ω= ɵ/t would be used, where ω is angular velocity (rad/s), theta is the angular displacement, and t is time (s). One revolution of the second hand is equal to 2π radians, or 2π/60s, so knowing this, we can apply onward. 1 radian= approx. 57 degrees.

The Attempt at a Solution

a) Va Second Hand= 2π/60s= 0.10471 rad/s= 6 deg/s
b) Va Minute Hand= 2π/3600s = 0.0017453 rad/s= 0.1 deg/s
c) Va Hour Hand= (2π /3600s)(60s)= 2.908 × 10-5 rad/s= 1.67 x 10-3 deg/s


Are the conversions and final values correct?

 

[ehild]

c) Va Hour Hand= (2π /3600s)(60s)= 2.908 × 10-5 rad/s= 1.67 x 10-3 deg/s

(2π /3600s)(60s)means multiplying (2π /3600s) by 60 s. It is displacement, not velocity. How much time is one revolution of the hour hand?

ehild

 

[eoneil]

One revolution of the hour hand is 12hrs.

a) Va Second Hand= 2π/60s= 0.1047 rad/s= 6 deg/s
b) Va Minute Hand= 2π/3600s = 0.001745 rad/s= 0.1 deg/s
c) Va Hour Hand= 2π /12(60s)(60s)= 1.45 x 10-4 rad/s= 8.33 x 10-3 deg/s

 

[cupid.callin]

c) Va Hour Hand= 2π /12(60s)(60s)= 1.45 x 10-4 rad/s= 8.33 x 10-3 deg/s

Its not (60s)(60s), its just (60)(60)s
By what way you wrote, answer would be in rad/s²

And for rad degree conversion, use: pi rad = 180 degree

 

[eoneil]

Ok, got it, (60)(60)s, giving rad/s^2. The converting angle to degrees = angle in radians x 180 / Pi

So for the hour hand, 2π /12(60)(60)s= 1.45 x 10-4 rad/s2= sqrt 1.45 x 10-4 rad/s2
final value is 1.20 x 10-4 rad/s, or 0.0069 deg/s