A rotating water pump works by taking water in at one side of a rotating wheel, and expelling it from the other side. If a pump with a radius of 0.120 m starts from rest and accelerates at 30.5 rad/s2, how fast will the water be traveling when it leaves the pump after it has been accelerating for 9.00 seconds

Explanation:

initial angular velocity, ωo = 0 rad/s

angular acceleration, α = 30.5 rad/s²

time, t = 9 s

radius, r = 0.120 m

let the velocity is v after time 9 s.

Use first equation of motion for rotational motion

ω = ωo + αt

ω = 0 + 30.5 x 9

ω = 274.5 rad/s

v = rω

v = 0.120 x 274.5

v = 32.94 m/s

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