What Is the Correct Radial Acceleration for a Spinning Wheel?

[student34]

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]

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?

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.]

 

[student34]

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.]

Thank-you so much. I left out a bunch of stuff because I didn't think that it was relevant - lesson learned on tweaking questions too.