PhYsIcS  RoTaTiOnAl MoTiOn
posted by Robert .
A tire (0.8 m diameter) starts at rest and has an angular acceleration of 5 rad/s^2. If it moves for 10 seconds and then stops abruptly causing a blob of mud at the top of the tire to fly off, how far along the ground will the blob travel until it hits the ground?

I know you use deltaTheta = 1/2(wi + wf)deltaT, but I don't know how to solve for the wf or t of the mud (the final velocity or the time it's in the air)

The tire's angular velocity when the mud flies off is Wf = 50 rad/s. Multiply that by the radius R for the horizontal velocity
The mud blob falls verically 0.8 m since it starts at the top of the tire. Use that fact to compute how long it takes to fall to the ground and how far it travels horizontally in that time. 
Oh, so you just convert the rotational motion into linear motion that can be used in a kinematic equation! Now I get it! Thanks!