Starting from rest, a disk rotates about its central axis with constant angular acceleration. in 6.00 s, it rotates 44.5 rad. during that time, what are the magnitudes of (a) the angular acceleration and (b) the average angular velocity? (c) what is the instantaneous angular velocity of the disk at the end of the 6.00 s? (d) with the angular acceleration unchanged, through what additional angle (rad) will the disk turn during the next 6.00 s?

a. The disk starts at rest, so its angular displacement at time is

It rotates 44.5 rad in this time, so we have

b. Since acceleration is constant, the average angular velocity is

where is the angular velocity achieved after 6.00 s. The velocity of the disk at time is

so we have

making the average velocity

Another way to find the average velocity is to compute it directly via

c. We already found this using the first method in part (b),

d. We already know

so this is just a matter of plugging in . We get

Or to make things slightly more interesting, we could have taken the end of the first 6.00 s interval to be the start of the next 6.00 s interval, so that

Then for we would get the same .

the speed of the cart after 3 seconds of low fan speed is ⇒ 54.0 cm/s.

the speed of the cart after 5 seconds of medium fan speed is ⇒ 120.0 cm/s.

the speed of the cart after 2 seconds of high fan speed is ⇒ 64.0 cm/s. 

just did the lab.