Direction of angular acceleration

AI Thread Summary
In the discussion about the direction of angular acceleration for a car slowing down on the XY plane, the key point is that the wheels have an angular velocity in the -x-direction. As the car decelerates, the angular acceleration must act in the opposite direction to the angular velocity, resulting in an angular acceleration in the +x-direction. The original poster initially struggled with the concept but later clarified their understanding by visualizing the problem. The problem was criticized for being poorly phrased, but the relationship between angular velocity and acceleration was ultimately grasped. Understanding the forces acting on the wheels helps clarify the direction of angular acceleration.
brendan3eb
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Homework Statement


Imagine a car driving on the XY plane in the +y-direction. If it is slowing down, in what direction is the angular acceleration of the wheels?

(a) the +x-direction
(b) the -x-direction
(c) the +y-direction
(d) the -y-direction
(e) the +z-direction

Homework Equations


a=αR

The Attempt at a Solution


I am just really lost when it comes to this problem. The apparent answer is A, but I do not understand why. I can't conceptualize angular acceleration with the axes..

The solution says the wheels have an angular velocity in the -x-direction and thus since the angular velocity is decreased the acceleration would be in the +x-direction. I get the second step, but I don't understand how you determine the angular velocity is in the -x-direction
 
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Actually, I think I get it now after messing around with some pictures..still, I think this was a stupid and poorly phrased problem.
 
think it as applying a force to stop the wheels...
 
Thread 'Variable mass system : water sprayed into a moving container'

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}...
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