Calculate the period and frequency of rotation

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SUMMARY

The discussion focuses on calculating the period and frequency of rotation for an object with a 2-meter diameter and an angular speed of 2.5 rad/s. The period is determined using the formula \( T = \frac{2\pi}{\omega} \), resulting in a period of approximately 2.51 seconds. Consequently, the frequency is calculated as \( f = \frac{1}{T} \), yielding a frequency of approximately 0.398 Hz. The calculations confirm the relationship between angular velocity, period, and frequency.

PREREQUISITES
  • Understanding of angular velocity and its units
  • Familiarity with circular motion concepts
  • Knowledge of trigonometric functions, specifically radians
  • Ability to manipulate basic algebraic equations
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  • Study the relationship between angular velocity and linear velocity
  • Explore the concept of centripetal acceleration in circular motion
  • Learn about different units of frequency and their applications
  • Investigate the effects of varying diameter on period and frequency
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Students studying physics, particularly those focusing on mechanics and rotational motion, as well as educators seeking to clarify concepts related to angular speed and periodic motion.

joe465
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Homework Statement



An object rotates in a circle of 2m diameter. The angular speed is 2.5 rad/s. Calculate the period and frequency of rotation.

Homework Equations



frequency=1/period

The Attempt at a Solution



That formula seem funny considering i need a value to work out the other. Is there another way to calculate either of these.

As far as i know:

period=time taken to complete one whole cycle

so would this work:

2*pie/w=t

2*pie/2.5=2.51s

Frequency = 1/period

frequency=1/2.51

=0.398

Not confident about this one but worth a try at least

Thanks, Joe
 
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Yep you've got it. The angular velocity is the amount of angle that is traveled through per second so by finding how many times that amount of angle goes into 2\pi radians you find the time taken (which is what you did).
 
Thanks for your reply, does frequency have a unit?
 

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