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.]
Radial acceleration is the acceleration that an object experiences as it moves in a circular path. It is directed towards the center of the circle and its magnitude depends on the speed and radius of the object's motion.
Radial acceleration can be calculated using the formula ar = v2/r, where ar is the radial acceleration, v is the speed of the object, and r is the radius of the circle.
Radial acceleration and tangential acceleration are two components of the total acceleration of an object moving in a circular path. Radial acceleration points towards the center of the circle, while tangential acceleration is perpendicular to the radial acceleration and tangent to the circle.
Radial acceleration causes the direction of an object's velocity to constantly change, resulting in circular motion. The greater the radial acceleration, the more the object's path deviates from a straight line.
Yes, radial acceleration can be negative. This occurs when the object's speed decreases or when it moves in the opposite direction of its initial motion, causing the acceleration to point in the opposite direction of the center of the circle.