Motion with Time-Dependent Angular Acceleration

[Zoubayr]

Homework Statement:

A sphere is initially rotating with angular velocity w_0 in a viscous liquid. Friction causes an angular deceleration that is proportional to the instantaneous angular velocity,α=-Aw, where A is a constant. Show that the angular velocity as a function of time is given by
w=w_0 exp(At)

Relevant Equations:

w=w_0 +∫α dt

I am not understanding how to even start the question

 

[BvU]

I am not understanding how to even start the question

This doesn't qualify as an attempt at solution, so PF isn't allowed to help...
https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

But perhaps a hint: write $\alpha = -\gamma \omega$ and there is your start !

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[haruspex]

write $\alpha = -\gamma \omega$

The info in post #1 says $\alpha = -A \omega$. Not sure how it helps to replace A with $\gamma$.
@Zoubayr , since you are given the target solution, it is easier to work backwards from there.

 

[Scottpm]

Often it helps to draw a picture of the problem. Then represent forces on any objects as arrows as the are vectors. You can do the same with accelerations and velocities, just make sure you don't confuse the different vectors.

 

[BvU]

Not sure how it helps to replace A with $\gamma$.

Oops, not thinking, too fast, etc...
Sorry about that.
Thanks for putting it right !

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