- #1
Grey_Thunderhead
- 7
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Homework Statement
“A bicycle wheel is mounted as in the lab and as shown to the right. This wheel has a mass of 6.55 kg, a radius of R = 38.0 cm, and is in the shape of a ring. A mass M = 1.85 kg is attached to the end of a string which is wrapped around an inner hub which has a radius r = 5.40 cm. Initially, the mass M is at a distance h = 72.0 cm above the floor. Assume friction is negligible.”
a. What will be the resulting angular acceleration of this wheel?
b. How long will it take for mass M to reach the floor?
c. What will be the total angular displacement of the wheel during the time in which the mass M is falling to the floor?
d. How much work was done on the wheel by the external torque as the mass M falls to the floor?
e. What will be the angular kinetic energy of this wheel just as mass M reaches the floor?
Homework Equations
τ = Iα
F=ma
a=αr
I=mr^2
The Attempt at a Solution
I thought that Tr = Iα, and since T is mg-ma, I rewrote it as r(mg-ma)=(mr^2)α. Then, I tried to just divide r(mg-ma) by mr^2 to get α.My process went like this:[r(mg-ma)] / (mr^2) = α
(mgr-mar) / (mr^2) = α
mr(g-a) / (mr^2) = α
(g-a)/r = αBut that doesn’t seem to be helping me very much, as I don’t know a.
Since the rest of the questions seem to be dependent upon the answer to Part A, I didn’t know whether or not to try them.
Thanks so much to anyone who helps. I think once I get Part A I’ll be able to do the rest