Angular acceleration of a wheel formula

AI Thread Summary
The formula for angular acceleration (α) can be derived from the known tangential acceleration (at) and the wheel's diameter (d) using the equation α = (2at)/d. The tangential speed (vt) can also be expressed in terms of the diameter as vt = (2ω)/d, where ω is the angular speed. The discussion emphasizes the relationship between tangential and angular values, particularly in the context of a wheel attached to a moving body, such as a car. It highlights the importance of understanding these conversions to solve problems involving angular acceleration. The conversation reflects a focus on applying known parameters to derive the necessary equations.
MrPotatoHead
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Homework Statement



What is the formula for angular acceleration, when the wheel's diameter, speed, acceleration and distance are known.

Homework Equations





The Attempt at a Solution

 
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The hard part is realizing that the speed the wheel is moving at (I'm assuming it's a wheel attached to a moving body like a car driving on the road) is equal to the tangential speed of a particle on the end of the wheel. Same can be said about acceleration.

So, then you simply convert between tangential and angular values, you said diameter is known, so these are given in terms of diameter d (with d=2r) as
\alpha=\frac{2a_{t}}{d}, \omega=\frac{2v_{t}}{d}
 
MrPotatoHead said:

Homework Statement



What is the formula for angular acceleration, when the wheel's diameter, speed, acceleration and distance are known.

Homework Equations





The Attempt at a Solution


Welcome to the PF.

You are asking for an equation for acceleration, when the acceleration is known?
 
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