How Do You Calculate the Constant Angular Acceleration of a Centrifuge?

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To calculate the constant angular acceleration of a centrifuge that rotates at 3500 rpm and completes 70 revolutions before stopping, the initial angular velocity must be converted to radians per second. The total angular displacement is calculated by multiplying the number of revolutions by 2π. Using the kinematic equation for rotational motion, the angular acceleration can be determined by rearranging the formula to solve for acceleration, considering the final angular velocity is zero. The result will indicate the direction of the angular acceleration based on the sign of the answer. This method provides a clear approach to solving the problem using established physics principles.
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A centrifuge in a medical laboratory rotates at an angular speed of 3500 rpm (revolutions per minute). When switched off, it rotates 70.0 times before coming to rest. Find the constant angular acceleration of the centrifuge. (Assume the initial direction of rotation is the positive direction. Indicate the direction with the sign of your answer.)
 
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Jared
 
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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