Finding Velocity for the Sweep-Second Hand of a Clock

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SUMMARY

The discussion focuses on calculating the average velocity and average acceleration of the tip of a clock's sweep-second hand, which is 3.1 cm long, over a 5.0-second interval. The average velocity can be determined by calculating the distance traveled in that time frame, knowing the hand completes a full rotation (360 degrees or 2π radians) in 60 seconds. The formula Distance = radius × angle (in radians) is essential for finding the distance traveled in 5 seconds, leading to the calculation of average velocity. Additionally, the average acceleration is found using the formula a = v²/r, and it is established that the angle between the average velocity and acceleration vectors is 90 degrees, as they are always perpendicular.

PREREQUISITES
  • Understanding of circular motion and angular displacement
  • Familiarity with the formula for average velocity
  • Knowledge of the relationship between linear and angular velocity
  • Ability to apply basic kinematic equations
NEXT STEPS
  • Calculate average velocity using Distance = radius × angle (in radians)
  • Explore the concept of angular velocity and its relation to linear velocity
  • Study the derivation of the formula a = v²/r for circular motion
  • Investigate the implications of perpendicular vectors in physics
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and circular motion, as well as educators looking for practical examples of velocity and acceleration calculations.

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Homework Statement



The sweep-second hand of a clock is 3.1 cm long.
What are the magnitude of (a) the average
velocity and (b) the average acceleration of the
hand’s tip over a 5.0-s interval? (c)what is the angel between the average velocity and acceleration vectors?


Homework Equations


a= v2/r


The Attempt at a Solution


Ok so I have been working on this problem for about an hour and its starting to annoy me I can't seem to find the velocity vector since I am not given a time frame besides the one for the acceleration. I know that I can find acceleration as soon as I find velocity but I don't have any formulas or any thought on how to go about solving for average velocity. I also know that the answer for part c is 90 degrees since they are always perpendicular so really its just part a that is giving me so much trouble.
 
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Here are a couple of hints: (1) The time frame for the velocity and the acceleration is the same: 5 sec. (2) Find the distance that the tip of the second hand travels in 5 sec. You can do this by knowing that it travels 360 degrees, or 2 Pi radians in 60 seconds. From that tells you can figure out the angle it travels in 5 sec. Then use Distance = radius times angle (in radians). That allows you to calculate the velocity and so on.
 
AEM said:
Here are a couple of hints: (1) The time frame for the velocity and the acceleration is the same: 5 sec. (2) Find the distance that the tip of the second hand travels in 5 sec. You can do this by knowing that it travels 360 degrees, or 2 Pi radians in 60 seconds. From that tells you can figure out the angle it travels in 5 sec. Then use Distance = radius times angle (in radians). That allows you to calculate the velocity and so on.

This was extremely helpful I forgot that you could find it in this way thank you so much.
 

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