MHB Angular Speed of Smaller Wheel

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To determine the angular speed of the smaller wheel, the relationship between the radii and angular speeds of both wheels must be established, given that they are connected by a belt. The linear velocity at the rim of both wheels must be equal, allowing for the calculation of the smaller wheel's angular speed using the formula v = rω. With the larger wheel's radius at 50 cm and its angular speed at 100 rpm, the linear velocity can be calculated. The smaller wheel's radius is 10 cm, and its angular speed can then be derived from the linear velocity. The discussion emphasizes the importance of understanding the connection between linear and angular velocities in this context.
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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