Calculating Angular Speed: Simple or Complicated?

AI Thread Summary
To calculate the instantaneous angular speed of a wheel accelerating from rest at 1.0 m/s², the correct approach involves converting linear acceleration to angular acceleration. The formula for final angular speed, which is based on linear acceleration, is not directly applicable since m/s² refers to linear, not angular acceleration. The relationship between linear and angular motion can be expressed as αr = a, where α is angular acceleration, r is the radius, and a is linear acceleration. By determining the linear velocity of the wheel's center after 0.10 seconds, one can derive the angular speed by considering the wheel's contact with the ground. Understanding these relationships clarifies the calculation of angular speed in this context.
angel_romano
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If a wheel accelerates from rest at 1.0 m/s^2 and I need to find the instantaneous angular speed of the wheel at .10s would this be the proper formula:

final angular speed=initial angular speed + angular acceleration(change in time)

When I use this formula, it comes out to .10 rad/s which just seems to simple.
 
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Well, you state the wheel accelerates from rest at 1.0m/s^2. m/s^2 is a measurement of linear acceleration not angular acceleration.
 
But how does the angular acceleration fit in then?

I have linear formulas, but I'm not sure which one I would use.
 
\alpha r = a
 
With a little bit of reasoning one could solve it with basic knowledge...
Via the linear acceleration one could calculate the linear velocity of the centre of the wheel after the given time. At this stage one could reason that the Earth is moving with the same speed in the opposite direction while the wheel is standing still, hence the speed of rotation of the wheel since it is in contact with the earth.
 
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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