What is the angular velocity of the drill bit in radians per second?

In summary, the conversation is about solving a problem for a cordless drill using the equations Nring*wring = Nsun*wsun and x = (5/6)*1440. The question is whether or not the solution is complete and what to do next, including converting revolutions per minute to radians per minute or per second.
  • #1
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Homework Statement


This problem is for a cordless drill.

[PLAIN]http://img718.imageshack.us/img718/8531/drill1.jpg


Homework Equations


[PLAIN]http://img442.imageshack.us/img442/3511/drill2.jpg

where N denotes number of teeth
w denotes angular velocity


The Attempt at a Solution


This is the work I have done so far:

[tex]\frac{9}{45} = \frac{x-720}{3600-x}[/tex]

[tex]\frac{3600-x}{5} = x-720[/tex]

[tex]x = \frac{5}{6}(1440)[/tex]

[tex]x = 1200 rpm[/tex]

I don't think I have completed the problem. Could someone please varify my work and show me what to do next?
 
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  • #2
Anyone?
 
  • #3
It appears to be correct, so far. One used Nring*wring = Nsun*wsun to obtain wring?

One has to convert revolutions per minute to radians per minute or per second. How many radians in a revolution?
 

Related to What is the angular velocity of the drill bit in radians per second?

1. What is drill bit angular velocity?

Drill bit angular velocity refers to the speed at which a drill bit rotates around its axis. It is typically measured in revolutions per minute (RPM).

2. How is drill bit angular velocity calculated?

To calculate drill bit angular velocity, you need to know the diameter of the drill bit and the RPM. The formula for calculating angular velocity is: angular velocity = (2π x RPM) / 60.

3. Why is drill bit angular velocity important?

Drill bit angular velocity is important because it determines how quickly the drill bit can cut through a material. Higher angular velocity means the drill bit will rotate faster and cut through the material more quickly.

4. How does drill bit size affect angular velocity?

Drill bit size directly affects angular velocity. The larger the diameter of the drill bit, the slower the angular velocity will be at the same RPM. This is because a larger drill bit has a larger circumference, so it must rotate more slowly to maintain the same linear speed at the cutting edge.

5. Can drill bit angular velocity be changed?

Yes, drill bit angular velocity can be changed by adjusting the RPM on the drill or by using different sized drill bits. Lowering the RPM will decrease the angular velocity, while increasing the RPM will increase the angular velocity.

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