Angular velocity of a machine problem

AI Thread Summary
A machine starts with an angular velocity of 1.6 rad/s and accelerates to 6.2 rad/s with an angular acceleration of 0.7 rad/s². To determine the number of revolutions made during acceleration and the time taken, the equations ω = ω₀ + αt and θ = θ₀ + ω₀t + 0.5αt² are utilized. The first equation helps find the time of acceleration, while the second calculates the total angular displacement in revolutions. The discussion highlights the importance of understanding the relationship between angular velocity, acceleration, and time in solving such problems. The equations provided are essential for approaching similar machine motion calculations.
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A machine rotates at an angular velocity of 1.6rad/s. Its velocity is then increased to 6.2rad/s at an angular acceleration of 0.7rad/s2. (a) How many revolutions does it make during its acceleration? (b) How long does the acceleration take?


Sorry I'm not quite sure as how to approach this problem, and I don't even know where to begin. Any advice would be greatly appreciated.
 
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Do you know any equation that relates revolutions, angular velocity, angular acceleration, and time? Can you then show some work? Thanks.
 
aright i got it thanks! i used:

\omega=\omega0+\alphat

and

\theta=\theta0+\omega0+\frac{1}{2}\alphat2
 

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