How Do You Convert Time into Radians and Calculate Rotational Acceleration?

[Stevo11]

Rotational Accel/Radians <<Solved>>

Homework Statement

Question 1)
18. Convert the following measurements to radians.

c) the motion of an hour hand in 4.4 h = 2.3 Rad
d) Earth’s rotation in 28.5 h = 7.5 Rad

<<<<<<figured it out, thanks SammyS for that obivious yet overlooked detail lol :D >>>>>>>>

Question 2)
A flywheel rotating at 18.0 rad/s slows to a
stop in 22.0 s. Find

a) its angular acceleration. = -18.18rad/sec^2
b) the number of radians it turns before
stopping. 198 rads
c) the number of cycles it completes in
this time. 31.5 Cycles
d) the angular speed after 8.7 s. 11rads/sec

though i have a feeling this isn't the end of my issues lol, if anyone knows of an awsome site/article anything on rotational work please let me know, because I've been searching lol

Thanks sammyS

-stevo

 

[SammyS]

How many radians does the hour hand pass through in 12 hours?

(Problem written BDC - Before Digital Clocks!) LOL

 

[SammyS]

Homework Statement

Question 2)
A flywheel rotating at 18.0 rad/s slows to a
stop in 22.0 s. Find

a) its angular acceleration. = -18.18rad/sec^2
b) the number of radians it turns before
stopping.
c) the number of cycles it completes in
this time.
d) the angular speed after 8.7 s.

The Attempt at a Solution

A)found the angular acceleration,(-.818 rad/sec/sec) but I can't figure out the rest of it...

B) I tried 18*22 to get the Rads before stopping, but that didn't work...

22 rad/s is the initial ang. vel. (It's not rotating at that rate the whole time.) The final ang. vel. is zero. Assuming a constant angular acceleration, what is the Average angular velocity? Use that. Then for (C), I would simply convert radians to cycles: 1 Cycle = 2π radians.

C) I tried dividing 18/6.28 to get the Cycles/second then multiplying by 22 seconds.. but that's not right either

D) well I don't know where to start...

I tried a lot of different things to solve these questions, most of my efforts are scribbled on papers littered around my room lol. I'm just so extremely frustrated and need some help/guidance, I don't want to be spoon fed though (I don't learn that way), just a nice push would help, or show me an example done? those are always best for me to learn, but I can't find any "like" examples of close problems.

This is our final Unit in Classical physics and my teacher's a..well let's not go there, he can't teach at all, so we're left to our own devices... I am so hopelessly lost its painful. I know what a radian is (from calculus) and I know that 2pi is one cycle, but I've never had so much issue with anything in physics before...

(My students have claimed to have the same problem.)

Kinematic equations are much like kinematic equations for linear motion (constant acceleration):

v=v_0+a\,t\quad\leftrightarrow\quad \omega=\omega_0+\alpha t

x-x_0=v_{avg}\ t=v_0\ t+(1/2)a\,t^2\quad\leftrightarrow\quad \theta-\theta_0=\omega_{avg}\ t=\omega_0 t+(1/2)\alpha t^2

v_{avg}=\frac{v+v_0}{2}\quad\leftrightarrow\quad\omega_{avg}=\frac{\omega+\omega_0}{2}

v^2={v_0}^2+\,2\,a(x-x_0)\quad\leftrightarrow\quad\omega^2={\omega_0}^2+\,2\,\alpha(\theta-\theta_0)

 

[Stevo11]

OH wow I solved it all! thank you SOOO much Sammys! how about you replace my teacher? haha! really though thank you so much for such a speedy and helpful response, much appreciated :D!