SOLUTION: A thin hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. Calculate the rotational kinetic energy at the bottom if the an

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A thin hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. Calculate the rotational kinetic energy at the bottom if the an      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1195923: A thin hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. Calculate the rotational kinetic energy at the bottom if the angular speed is 2.0 rad/s at that position. [Moment of inertia of thin hoop, I = MR^2, M = mass and R = radius of hoop](2 Points)

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

The connecting formula you need is:
+E%5Brot%5D+=+%281%2F2%29Iw%5E2+ I will use w for ω (omega, normally this is used for angular speed), due to problems rendering...
Substituting for I:
+E%5Brot%5D+=+%281%2F2%29%28Mr%5E2%29w%5E2+
= +%281%2F2%29%280.2kg%29%280.5m%29%5E2%2A%282+rad%2Fs%29%5E2+
= ++0.1+ kg%2Am%5E2%2Fs%5E2+
= +0.1++ Joule