Equations for rotational motion with constant acceleration

[DH214]

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 35.0 rad/s2, how fast will the water be traveling when it leaves the pump after it has been accelerating for 9.00 seconds?

 

[djeitnstine]

$$\alpha$$ is measured in radians per second sqared $$(rad s^{-2} )$$ my guess is that you are either trying to find the angular velocity or the linear velocity.

angular acceleration = $$\alpha = \frac{\Delta \omega}{t}$$
angular velocity = $$\omega = \frac{\Delta \theta}{t}$$

the relationship between linear velocity/acceleration and angular velocity/acceleration is

linear velocity v

radius r

$$v= r \omega$$ m/s

$$a= r \alpha$$ m/$$s^{2}$$