Connected Wheels Problem. Angular Velocity.


by EpiphoneBenji
Tags: angular velocity, connected wheels
EpiphoneBenji
EpiphoneBenji is offline
#1
Sep18-11, 03:59 PM
P: 2
1. The problem statement, all variables and given/known data
Wheel A of radius ra = 8.9 cm is coupled by belt B to wheel C of radius rc = 30.7 cm. Wheel A increases its angular speed from rest at time t = 0 s at a uniform rate of 8.6 rad/s2. At what time will wheel C reach a rotational speed of 93.0 rev/min, assuming the belt does not slip?


2. Relevant equations
2 π rad = 1 Rev
v = vo + at ( constant acc)

3. The attempt at a solution
Wheel A and Wheel C have the same velocity, so I converted the rads to revs and 93 rev/min to 1.55 revs/s and divided the velocity by the acceleration to find the time. But the answer doesn't work. Am I doing something wrong ? Please help !

Thanks
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jncarter
jncarter is offline
#2
Sep18-11, 04:49 PM
P: 49
We need to see more of your work to know just were you went wrong. Also, note that the time to for wheel A to complete one revolution is much less than that of wheel B, yet both go through 2[itex]\pi[/itex] radians and your work thus far does not take this difference into account.
EpiphoneBenji
EpiphoneBenji is offline
#3
Sep18-11, 05:05 PM
P: 2
But being attached to a string doesn't mean they are going at the same speed ?

jncarter
jncarter is offline
#4
Sep18-11, 10:20 PM
P: 49

Connected Wheels Problem. Angular Velocity.


Define "speed". Each point on the belt will be be moving at the same rate, but translational velocity and angular velocity are not the same. Your conversion from radians to revs needs to include the fact that angular velocity depends on radius. Try looking up the conversion of tangential velocity to angular on wikipedia.


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