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