Motion with Time-Dependent Angular Acceleration

AI Thread Summary
The discussion centers on understanding a problem involving motion with time-dependent angular acceleration. A participant expresses confusion about how to start solving the question. A hint is provided, suggesting the use of the equation α = -γω as a starting point. Another participant points out that the original information states α = -Aω and questions the relevance of substituting A with γ. The conversation emphasizes the importance of visualizing the problem and accurately representing forces and vectors.
Zoubayr
Messages
24
Reaction score
2
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
 
Physics news on Phys.org
BvU said:
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.
 
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.
 
haruspex said:
Not sure how it helps to replace A with ##\gamma##.
Oops, not thinking, too fast, etc...
Sorry about that.
Thanks for putting it right !

##\ ##
 
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Thread 'Minimum mass of a block'
Here we know that if block B is going to move up or just be at the verge of moving up ##Mg \sin \theta ## will act downwards and maximum static friction will act downwards ## \mu Mg \cos \theta ## Now what im confused by is how will we know " how quickly" block B reaches its maximum static friction value without any numbers, the suggested solution says that when block A is at its maximum extension, then block B will start to move up but with a certain set of values couldn't block A reach...
Back
Top