Solution Found!
(a) Derive an equation for the radial acceleration that
Chapter 11, Problem 26E(choose chapter or problem)
(a) Derive an equation for the radial acceleration that includes v and \(\omega\), but not r. (b) You are designing a merry-go-round for which a point on the rim will have a radial acceleration of \(0.500\ \mathrm{m/s}^{2}\) when the tangential velocity of that point has magnitude 2.00 m/s. What angular-velocity is required to achieve these values?
Questions & Answers
QUESTION:
(a) Derive an equation for the radial acceleration that includes v and \(\omega\), but not r. (b) You are designing a merry-go-round for which a point on the rim will have a radial acceleration of \(0.500\ \mathrm{m/s}^{2}\) when the tangential velocity of that point has magnitude 2.00 m/s. What angular-velocity is required to achieve these values?
ANSWER:Step 1 of 3
To derive an equation for radial acceleration
When a particle moves in a circular path, the acceleration is passed through the center of the circle and known as centripetal acceleration. It acts radially inward.
The expression for radial acceleration \(\mathrm{a}=\frac{v^{2}}{r}\) ----(1)
Where
v - linear velocity or tangential velocity
r - radius of the circular path