- #1
Julie323
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Homework Statement
A 44.0-cm diameter wheel, consisting of a rim and six spokes, is constructed from a thin rigid plastic material having a linear mass density of 25.0 g/cm. This wheel is released from rest at the top of a hill 56.0 high.
How fast is it rolling when it reaches the bottom of the hill?
How would your answer change if the linear mass density and the diameter of the wheel were each doubled?
Homework Equations
I of a hoop=mr^2
I of a rod=1/12 ML^2
The Attempt at a Solution
I set mgh=.5Iw^2 Inertia=m(rim)r^2+6(1/12 ML^2). I found the mass of the rim by finding the circumference and multiplied it by the density giving me 3.456 kg, plugged .22 m in for the radius. Then I found the mass of a spoke by multiplying .44cm by 2.5 g/cm which gave me 1.1 kg. I plugged that in with L being .44. This gave me an inertia of .274. This made the energy equation (10.056)(9.8)(56)=.5(.274)w^2. Solving for w gave me 200.2 rad/s which I then multiplied by .22 to give me a velocity of 44.2 m/s. But that was wrong. Where did I go wrong? Thanks so much!