1. ## angular displacement

After 10.0 s, a spinning roulette wheel at a casino has slowed down to an angular velocity of +1.82 rad/s.

During this time, the wheel has an angular acceleration of -4.25 rad/s2.

Determine the angular displacement of the wheel.

...

so is 1.82 rad/s the w0 or the wf?

and i'm trying to find theta i believe.

2. Originally Posted by rcmango
After 10.0 s, a spinning roulette wheel at a casino has slowed down to an angular velocity of +1.82 rad/s.

During this time, the wheel has an angular acceleration of -4.25 rad/s2.

Determine the angular displacement of the wheel.

...

so is 1.82 rad/s the w0 or the wf?

and i'm trying to find theta i believe.
$\frac{d^2}{dt^2}\theta = -4.24$

so:

$\frac{d}{dt}\theta = -4.24t + \theta'_0$

$
\theta=\frac{-4.24 t^2}{2}+\theta'_0 t + \theta_0
$

We may assume that $\theta_0=0$ so we have:

$
\theta=\frac{-4.24 t^2}{2}+\theta'_0 t
$

Now put in your values and if needed reduce the result modulo $2\pi$.

Note you are give $\theta_{t=10}=1.82$ rather than the value of $\theta_{0}$, so you will have to work that out.

RonL

3. what is theta' ?

4. Originally Posted by rcmango
what is theta' ?
$\theta'$ is angular velocity

RonL

5. i think you gave me an infraction point because you mis understood my question, which is

what is theta ' what is the purpose in other words.

the theta with the '

there are two thetas?

okay i got it 231 rad

thankyou.

6. Originally Posted by rcmango
i think you gave me an infraction point because you mis understood my question, which is

what is theta ' what is the purpose in other words.

the theta with the '

there are two thetas?

okay i got it 231 rad

thankyou.
I don't know if you are in a Calculus class? $\theta ^{\prime}$ is the time derivative of $\theta$. You would call it the angular velocity.

-Dan

7. Originally Posted by rcmango
After 10.0 s, a spinning roulette wheel at a casino has slowed down to an angular velocity of +1.82 rad/s.

During this time, the wheel has an angular acceleration of -4.25 rad/s2.

Determine the angular displacement of the wheel.

...

so is 1.82 rad/s the w0 or the wf?

and i'm trying to find theta i believe.
As always, start with a coordinate system. I'm going to set an origin for $\theta$ to be at the point where the 10 s time interval started. (There is a direction for the angular displacement, but I'm going to assume that you haven't seen this yet and skip it.)

Here's what we know:
$t = 10~s$
$\theta _0 = 0~rad~~~~\theta =$?
$\omega_0 =$? $~~~~\omega = 1.82~rad/s$
$\alpha = -4.25~rad/s$

We want $\theta$. Typically I simply apply one of my four "master" equations to solve this kind of problem, but all of them depend on a value of $\omega _0$:
$\theta = \theta _0 + \omega _0t + \frac{1}{2} \alpha t^2$

$\theta = \theta _0 + \frac{1}{2}( \omega _0 + \omega )t$

$\omega = \omega _0 + \alpha t$

$\omega ^2 = \omega _0^2 + 2 \alpha ( \theta - \theta _0 )$

(Since this kind of situation doesn't happen very often I don't keep an equation for it in my back pocket, as it were.)

So we need to use an equation to find $\omega _0$, then use another to find $\theta$.

Well:
$\omega = \omega _0 + \alpha t$

$\omega_0 = \omega - \alpha t = 1.82 - (-4.25)(10) = 44.32~rad/s$

And thus
$\theta = \theta _0 + \omega _0t + \frac{1}{2} \alpha t^2$

$\theta = (44.32)(10) + \frac{1}{2} (-4.25) (10)^2 = 230.7~rad$

-Dan

8. thankyou, ya i recognized the derivative, i just wasn't sure which theta to solve for the actual angular velocity.

9. Originally Posted by rcmango
i think you gave me an infraction point because you mis understood my question, which is

what is theta ' what is the purpose in other words.

the theta with the '