The radial acceleration of a wheel with a radius of 0.2 m and a constant angular acceleration of α = 3.00 rad/s² is not constant and changes over time. The initial calculation of radial acceleration as 1.2 m/s² is based on the assumption that the wheel starts from rest and rotates through an angular distance of 1 radian, which was not specified in the problem statement. The book's value of 15.1 m/s² is likely derived from a different context or additional information not provided in the original question.
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student34 said:Homework Statement
A wheel with a radius of 0.2 m has a constant angular acceleration of α = 3.00 rad/s^2. Find the radial acceleration.
Homework Equations
arad = ω^2*r
ω^2 = ωo^2 + 2*α(θ - θo) → ω = √(2*α*θ)
The Attempt at a Solution
ω = √6 rad/s → a rad = 6*0.2 m/s^2 = 1.2 m/s^2
The book has 15.1 m/s^2. Is the book wrong?
collinsmark said:Are you leaving something out of the problem statement?
With a constant angular acceleration, the radial acceleration is not constant. It will change with time.
In your attempted solution, you found the radial acceleration assuming that the wheel starts from rest, and after the wheel rotated an angular distance of 1 rad. Yet none of that was given in the problem statement.
Is something missing?
[Edit: the tangential acceleration will be constant though. But that's not 15.1 m/s2 either.]