Angular Speed of Smaller Wheel

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SUMMARY

The discussion focuses on calculating the angular speed of a smaller wheel when connected to a larger wheel via a belt. Given a radius of 10 cm for the smaller wheel and 50 cm for the larger wheel, with the larger wheel's angular speed at 100 rpm, the relationship between the linear velocities of both wheels is crucial. The linear velocity of the outer rim of both wheels must be equal, allowing for the determination of the smaller wheel's angular speed in radians per minute. The user plans to share their calculations later for further clarification.

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  • Understanding of angular speed and linear velocity concepts
  • Familiarity with the relationship between radius and angular speed
  • Basic knowledge of radians and revolutions per minute (rpm)
  • Experience with belt-driven systems in mechanical contexts
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  • Study the relationship between angular speed and linear velocity in rotating systems
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mathdad
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I decided to change the radius.

Let r = radius

If r = 10 cm, R = 50 cm, and the angular speed of the larger wheel is 100 rpm, determine the angular speed of the smaller wheel in radians per minute.

What are the steps to solve this question?
 
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I am assuming one wheel drives the other via a belt. As such, what to we know about the linear velocity of points on the outer rim of both wheels?
 
I will post my work for this question tonight after work.
 

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