What is the Constant Angular Velocity of a Watch's Second Hand?

  • Context: Undergrad 
  • Thread starter Thread starter ehabmozart
  • Start date Start date
  • Tags Tags
    hand Omega
Click For Summary
SUMMARY

The constant angular velocity of a watch's second hand is calculated as 2π radians per 60 seconds, which simplifies to π/30 radians per second. The discussion clarifies that the second hand does not experience angular acceleration; rather, it maintains a constant angular velocity throughout its motion. The confusion arises from misapplying the formula for angular displacement that includes angular acceleration, which is unnecessary in this case. Therefore, the correct interpretation is that the second hand completes one full revolution every minute without any change in its angular velocity.

PREREQUISITES
  • Understanding of angular velocity and angular displacement
  • Familiarity with basic rotational motion concepts
  • Knowledge of radians and their application in circular motion
  • Ability to apply kinematic equations for rotational motion
NEXT STEPS
  • Study the principles of rotational dynamics in physics
  • Learn about angular acceleration and its implications in different scenarios
  • Explore the relationship between linear and angular velocity
  • Investigate the applications of angular motion in real-world mechanisms
USEFUL FOR

Physics students, educators, and anyone interested in understanding the mechanics of rotational motion, particularly in the context of everyday objects like watches.

ehabmozart
Messages
212
Reaction score
0
omega of the second hand??

Consider a second hand in the watch. What is the constqant angular velocity.
Logicaly, i would say it travels through 1 rev in 1 min so, it is 2∏/60
However, if we look it on the other way, it has angular acceleration
so theta= (w node + w final)/2 * t gives 2∏/30 .. Where is my mistake??
 
Physics news on Phys.org


ehabmozart said:
Consider a second hand in the watch. What is the constqant angular velocity.
Logicaly, i would say it travels through 1 rev in 1 min so, it is 2∏/60
OK.
However, if we look it on the other way, it has angular acceleration
What other way? The angular velocity is constant.
so theta= (w node + w final)/2 * t gives 2∏/30 .. Where is my mistake??
What are you solving for? Using this you'll find an angular displacement of 2π radians in 60 seconds.
 

Similar threads

Undergrad How can angular displacement be larger than 2pi?
  • · Replies 20 ·
Replies
20
Views
3K
Undergrad Curl of velocity vector in rotational motion
  • · Replies 9 ·
Replies
9
Views
967
Undergrad Angular velocity of a rod and what formula to use while solving.
  • · Replies 15 ·
Replies
15
Views
3K
Undergrad How Does Angular Velocity Affect Instantaneous Acceleration in Rotating Systems?
  • · Replies 1 ·
Replies
1
Views
1K
High School Sign conventions in torque and non-uniform circular motion
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad I'm calculating more energy out than I put in
  • · Replies 138 ·
5
Replies
138
Views
9K
Undergrad Lagrangian for pendulum
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Non-Constant Angular Acceleration
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Conceptual questions about Angular Momentum Conservation and torque
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Alternative Approach to Solving Foucault's Pendulum Behavior
  • · Replies 8 ·
Replies
8
Views
2K