Angular Speed of Smaller Wheel

In summary, the angular speed of a smaller wheel is the rate at which the wheel rotates per unit time. It can be calculated by dividing the angular displacement by the time taken for the wheel to complete one revolution. Angular speed is typically measured in radians per second (rad/s) or degrees per second (deg/s). The size of the smaller wheel can affect its angular speed, with a smaller wheel having a faster angular speed if they both have the same angular displacement and time. Additionally, the angular speed of a smaller wheel is directly proportional to its linear speed, with an increase in angular speed resulting in an increase in linear speed. The exact relationship between angular speed and linear speed depends on the radius of the smaller wheel.
  • #1
mathdad
1,283
1
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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  • #2
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?
 
  • #3
I will post my work for this question tonight after work.
 

FAQ: Angular Speed of Smaller Wheel

What is the angular speed of a smaller wheel?

The angular speed of a smaller wheel is the rate at which the wheel rotates per unit time.

How is the angular speed of a smaller wheel calculated?

The angular speed of a smaller wheel can be calculated by dividing the angular displacement by the time taken for the wheel to complete one revolution.

What units is angular speed measured in?

Angular speed is typically measured in radians per second (rad/s) or degrees per second (deg/s).

Does the size of the smaller wheel affect its angular speed?

Yes, the size of the smaller wheel can affect its angular speed. A smaller wheel will have a faster angular speed than a larger wheel if they both have the same angular displacement and time.

How is the angular speed of a smaller wheel related to its linear speed?

The angular speed of a smaller wheel is directly proportional to its linear speed. This means that as the angular speed increases, the linear speed also increases. The exact relationship between angular speed and linear speed depends on the radius of the smaller wheel.

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