What is the relationship between angular velocity and tangential velocity?

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Homework Help Overview

The discussion revolves around the relationship between angular velocity and tangential velocity in the context of a discus throw. The problem involves calculating the speed of the discus at release after one complete revolution, given the diameter of the circular path and the time taken for the revolution.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the calculation of angular acceleration and its implications for finding tangential velocity. There are attempts to clarify the relationship between angular and tangential velocity, with some questioning the correctness of the angular acceleration value derived.

Discussion Status

Participants are actively engaging with the problem, with some providing hints and guidance on how to approach the conversion from angular to tangential velocity. There is a recognition of the need to express the final answer in meters per second, which has led to further exploration of the relevant equations.

Contextual Notes

Participants note the requirement to convert angular measurements to linear speed, highlighting the challenge of transitioning from radians per second to meters per second in their calculations.

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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