Question

rotational kinematics

Answer 1

A wheel is rotating about an axis that is in the z-direction. the angular velocity is -6 rad/s at t=0, increases linearly with time and is 8.00 rad/s at t=7s. counterclockwise rotation is positive. find the duration of the time interval when the speed of the wheel is increasing.

Answer 2

find the duration of the time interval when the speed of the wheel is decreasing. what is the angular displacement of the wheel at 7s.

Answer 3

a little lost right now...

Answer 4

-6 rad/s are in the clockwise direction and 8 rad/s are in the counterclockwise direction (notice the change is signs).

Therefore the angular velocity is decreasing when it goes from -6 rad/s to 0, and it is increasing when it goes from 0 to 8 rad/s.

The angular displacement is the circular path that it follows. As it goes from -6 to 8, there was a change in motion: an acceleration. If you find that acceleration you can find the circular displacement using one of the kinematics equations.

Answer 5

angular velocity is \[\alpha=\frac{\Delta \omega}{\Delta t}=\frac{[8-(-6)]}{7-0}=2\frac{rad}{s^2}\]

Answer 6

so i just use \[\Delta \theta=\omega_{0}t+\frac{1}{2}\alpha t^2\]right?

Answer 7

Yep. \( \omega_0\) is negative but \( \alpha\) is positive, so all fit together.

Answer 8

hmmm so to find the angular displacement do i have to find the angular distance it goes in one way then the distance it goes in the other and then take the difference of those?

Answer 9

or rather i can't do that since i don't know the angular acceleration at t=0

Answer 10

Just curious, should the question:
...what is the angular displacement of the wheel at 7s.
read
...what is the angular displacement of the wheel over the 7s. ??

Answer 11

hmm... well it's exactly as i wrote. maybe it's asking for the displacement after the wheel stops decreasing in speed.

Answer 12

Nop. I think I've confused two thing. Angular displacement is \(\Delta \theta\). Linear displacement in circular motion is what I said, which is \(\Delta s\) (the arc length). You are asked to find the former, not the latter.

Sorry about that.

We are supposing that the acceleration from -6 rad/s to 8 rad/s was constant. So the last equation que be used to figure out \(\Delta \theta\).

Answer 13

Angular Displacement would be over a specified amount of time.
Angular Velocity can be determined at a specific time, e.g. "at 7s".

Answer 14

well i don't know. i have to catch the city bus and i wont be able to finish this until after the due time of 5pm so i'm just going to close this. thanks anyway guys.

Answer 15

Okey (: