Velocity and acceleration problem

AI Thread Summary
The discussion focuses on a physics problem involving a rolling wheel with constant acceleration. The key point is to demonstrate that the acceleration of any point on the wheel can be expressed using the formula (a_{0}^2 + v^4/b^2)^\frac{1}{2}, indicating that translational and angular accelerations are perpendicular. The second part of the problem requires showing the ground-relative acceleration using a more complex formula that incorporates the angle theta, which represents the position of a point on the wheel. Understanding theta is crucial for solving the problem, as it affects the resultant acceleration. Overall, the discussion emphasizes the need to analyze both translational and angular components to find the resultant acceleration.
thenewbosco
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hello i am not sure how to even begin this problem (i.e. how to set it up)

A wheel of radius b, rolls along the ground with constant forward acceleration a0. Show that, at any given instant, the magnitude of the acceleration of any point of the wheel is (a_{0}^2 + \frac{v^4}{b^2})^\frac{1}{2}

The second part asks to show the magnitude of the acceleration relative to the ground is a_{0}[2 + 2cos\theta + \frac{v^4}{a_{0}^2 b^2} - (\frac{2v^2}{a_{0}b})sin\theta]^\frac{1}{2}
Here v is the instantaneous forward speed and theta defines the location of the point on the wheel, measured forward from the highest point.

Could someone help me get started on this as well as explain what theta is, since i do not understand based on the question.
 
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The problem is one of finding the resultant acceleration for two components, the translational acceleration a_0 and the angular acceleration v^2/r.

The formula (a_{0}^2 + \frac{v^4}{b^2})^\frac{1}{2}
implies that the two accelerations are mutually perpendicular, so one would use the square root of the sum of the squares, but the second part implies r = b, i.e. it applies to the points on the circumference.
 
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