What are the rotational motion problems and how to solve them?

[Twilit_Truth]

OK, I can't figure this out either. Sorry if it seems I'm here a lot, I'm trying to make up 6 weeks worth of work. I have 4 problems here. I have no idea how to even begin these problems, so ANYTHING would be helpful. (s^2 is seconds squared)


1) A wheel rotates with a constant acceleration of 3.50 rad/s^2. If the angular speed of the wheel is 2.00 rad/s at ti = 0:

a) Trough what angle does the wheel rotate in 2.00s?

b) What is the angular speed at t = 2.00s?


2) Mateo rode a unicycle with a wheel diameter of .406m. If the wheel's average angular acceleration was 0.552 rad/s^2, how long will it take for the wheel's angular speed to increace from 2.39 rad/s to 5.20 rad/s?


3) In the biblical story, little David slew the Giant Goliath with a sling shot. Assume that David starts rotating a .150 kg stone from rest in a sling of radius 1.50 m. If the average angular acceleration of the stone is 4.5 rad/s^2:

a) What is the tension in the sling after 8.5 s?

b) What is the linear velocity of the stone if he releases it at 8.5 s?


4) In a typical CD player, the disc spins counterclockwise, and the speed of the surface at the point of contact of the laser lens is 1.3 m/s. This requires that the rotational speed vary with the radiuis of the track being played.

a) Find the angular speed of the disc in both rad/s and RPM (rotations/min.) when information is being read from the innermost track (r = 23 mm) and the outermost track (r = 58 mm)

b) The maximum playing time of a standard music CD is 74 min. 33 s. How many revolutions does the disc make during that time? Assume constant angular acceleration.

c) What is the total length of the track that is read by the laser during the 74 min. 33 s of playing time?

I know it's a lot, but I'm going to fail if I don't get help. Thank you for your time.

 

[awvvu]

These are pretty basic rotational motion problems. All you need to solve them are the kinematics equations for rotation. #3 involves circular motion.

Show some work.

 

[hage567]

Look at this site:

http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.html#drot

See if it helps.

 

[Twilit_Truth]

It should. Thank you so much.

 

[Twilit_Truth]

Uh, how do I find the tension in problem 3? I never was good at tension.

 

[hage567]

Do you know what centripetal force is?

 

[Twilit_Truth]

Ah. thank you for the help.

 

[Twilit_Truth]

How do you convert rad/s into rpm?

 

[Shooting Star]

Think how many rads are there in one rev.

 

[Twilit_Truth]

2pi, right?

 

[Shooting Star]

Right. Now you can convert?

 

[Twilit_Truth]

ok, so if 2pi rad/s =60 RPMs, then I take the rad/s and multiply by 60, then divde by 2pi?

 

[Shooting Star]

Yes.

Think a while, gather 3-4 questions, and then post. Saves time and energy.

 

[Twilit_Truth]

Alright, thanks for the help. This really saved my butt.

 

[Twilit_Truth]

Ok, back with more questions. On problem 4, part b, how do you find the number of revolutions wothout a measure of the track length (which is found in c, and I need help with that too)?

 

[Shooting Star]

Do you know the rotational equivalents of the eqns of uniform linear accn? There's one connecting initial and final velocities, and the dist. Can you the apply the equivalent of that for 4 b?