What is the relationship between angular velocity and tangential velocity?

AI Thread Summary
The discussion revolves around calculating the tangential velocity of a discus thrown by an athlete who completes one revolution in one second. The diameter of the circular path is 1.7 meters, leading to a radius of 0.85 meters. The angular acceleration was initially calculated incorrectly but later corrected to 6.28 rad/s². To find the tangential velocity, the relationship between angular velocity and tangential velocity is highlighted, emphasizing the need to convert radians per second to meters per second. Understanding the conversion and the formulas involved is crucial for determining the speed of the discus at release.
rebeccc
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Homework Statement


To throw the discus, the thrower holds the discus with a fully outstretched arm and makes one revolution as rapidly as possible to give maximum speed to the discus at release. The diameter of the circle in which the discus moves is about 1.7m.

If the thrower takes 1.0s to complete one revolution, starting from rest, what will be the speed of the discus at release?



Homework Equations





The Attempt at a Solution

I found the angular acceleration to be 2pi rad/s. I just don't know how to find the speed from there..
 
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Hi rebeccc,


rebeccc said:

Homework Statement


To throw the discus, the thrower holds the discus with a fully outstretched arm and makes one revolution as rapidly as possible to give maximum speed to the discus at release. The diameter of the circle in which the discus moves is about 1.7m.

If the thrower takes 1.0s to complete one revolution, starting from rest, what will be the speed of the discus at release?



Homework Equations





The Attempt at a Solution

I found the angular acceleration to be 2pi rad/s. I just don't know how to find the speed from there..

I don't believe that angular acceleration is correct. What equations and numbers did you use to find it?
 
Okay, I re-worked it and found the angular acceleration to be 6.28 rad/s^2. I just don't know where to go from here to find the speed of the discus when it is released...
 
If anyone has any ideas.. I need help asap!
 
assuming your angular acceleration is correct. You can use the formula

\omega_f = \omega_i + \alpha t
 
I have to have my answer in m/s which is really throwing me off.. I don't know how to get to m/s from rad/s. = (
 
Ahh so it wants the tangential velocity.
well think about what omega is.
It's radians per second. Then think about exactly what a radian is.

Hint:
1 radian is the arc length of the radius, so the total length of 1 radian = that of the radius.

Hint #2:
therefore omega = v/r
 

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