- #1
etotheipi
- Homework Statement
- See below
- Relevant Equations
- N/A
Hey guys, I need to check that I'm not doing something stupid. You have two uniform disc-shaped gears, one of which has twice the radius of the other [and 16 times the moment of inertia]. Initially, the larger gear is spinning at ##\omega##, and then they're suddenly meshed together. We need to show that the angular speed of the larger disk drops by 20%. [Edit. To clarify, the disks are given to have equal uniform area densities ##\sigma##].
Since the torque of the tangential force on the larger disk about its centre is twice in magnitude compared to the torque of the tangential force on the smaller disk about its centre, I reckoned that the change in angular momentum of the larger one would be twice that of the smaller one, i.e. that ##16(\omega - \omega_f) = 2\omega_f##. But that gives me that ##\omega_f = (8/9)\omega##, which clearly isn't a 20% decrease.
What did I miss?! It's almost completely improbable that the question contains a mistake, so the error must be on my end. Thanks!
Since the torque of the tangential force on the larger disk about its centre is twice in magnitude compared to the torque of the tangential force on the smaller disk about its centre, I reckoned that the change in angular momentum of the larger one would be twice that of the smaller one, i.e. that ##16(\omega - \omega_f) = 2\omega_f##. But that gives me that ##\omega_f = (8/9)\omega##, which clearly isn't a 20% decrease.
What did I miss?! It's almost completely improbable that the question contains a mistake, so the error must be on my end. Thanks!
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