Uniform Circular Motion in a Watch

In summary, we are given the length of the second hand on a watch and its revolution time. We need to find the speed of the end of the second hand in uniform circular motion. Using the equation ac=v^2/r and the relationship between speed and angular velocity, we can solve for the speed by first calculating the angular velocity using the given revolution time.
  • #1
eagles12
76
0

Homework Statement



The second hand on a watch has a length of 4.5mm and makes one revolution in 60s. What is the speed of the end of the second hand as it moves in uniform circular motion?


Homework Equations



ac=v^2/r

The Attempt at a Solution



ac=v^2/4.5
 
Physics news on Phys.org
  • #2
speed = distance/time
How far does the end of the hand move in 1 revolution?
How long does that take?
 
  • #3
The equation you need to use here is:
v = ωr
Where ω is angular velocity.

The angular velocity is given by:
ω = Δθ / Δt

Thus the angular velocity of the second hand is known from the statement of your problem. Hope this helps.
 

1. What is uniform circular motion in a watch?

Uniform circular motion in a watch refers to the motion of the watch's hands as they move around the dial at a constant speed. It is called "uniform" because the speed is consistent, and "circular" because the motion follows a circular path.

2. How does a watch maintain uniform circular motion?

A watch maintains uniform circular motion through the use of a small, precisely crafted mechanism called the escapement. The escapement allows the watch's hands to move in small, equal increments, keeping the motion uniform and consistent.

3. What is the role of centripetal force in a watch's circular motion?

The centripetal force in a watch's circular motion is provided by the tension in the watch's spring, also known as the mainspring. This force keeps the watch's hands moving in a circular path around the dial.

4. How does the size of a watch affect its uniform circular motion?

The size of a watch does not have a significant impact on its uniform circular motion. As long as the watch's components, such as the escapement and mainspring, are properly sized and calibrated, the motion will remain uniform regardless of the watch's size.

5. Can a watch's circular motion ever become non-uniform?

Yes, a watch's circular motion can become non-uniform if the watch's components become damaged or if the watch is not properly maintained. For example, a bent or damaged escapement can cause the hands to move at varying speeds, resulting in non-uniform circular motion.

Similar threads

  • Introductory Physics Homework Help
2
Replies
55
Views
655
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
163
  • Introductory Physics Homework Help
Replies
7
Views
2K
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
935
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
9
Views
6K
  • Introductory Physics Homework Help
Replies
30
Views
500
Back
Top