# Find angular acceleration using theoretical values

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1. Mar 2, 2015

### Thynazgul

1. The problem statement, all variables and given/known data
I'm doing a coursework where I must find the angular acceleration of a rolling tin can using theoretical values. I have its mass and radius. I actually have experimental data so i have access to the actual values of angular velocity and angular acceleration, as well as time.

2. Relevant equations
acceleration = torque / moment of inertia
moment of inertia = 1/2mr2
v= square root (gh)
angular acceleration = change in angular velocity / change in time

3. The attempt at a solution
I'm really stuck but I thought of calculating the linear velocity by using mgh= 1/2mv2, then using the velocity and radius to calculate the angular velocity. Once I have that I could calculate two angular velocities and use the time between them to measure the acceleration.

Another attempt was to use a = torque / I and try to calculate the torque but I don't know what force to use. I believe it could be friction but I do not have information on friction.

2. Mar 2, 2015

### brainpushups

What exactly is the condition for which you are trying to calculate the angular acceleration? I assume that the can is rolling down an incline, but that isn't clear from your post.

3. Mar 2, 2015

### Thynazgul

Exaclty, sorry I forgot to mention that.

4. Mar 2, 2015

### Thynazgul

Since I have a measured value for linear velocity I've been playing around with angular momentum,
since L= Iω and L=mvr
then Iω =mvr
ω=mvr / I

maybe I can do somethin with that but I would prefer to calculate a value for linear velocity. I found a formula that rearranges mgh = KE + rotational KE into something like root(gh) but it makes no sense since the height change could be the same but at different velocities...

5. Mar 2, 2015

### brainpushups

If you're trying to find a formula for the acceleration this is the approach you'll want to take. Friction is indeed an unknown (along with the acceleration), but that is okay. You have two equations F=ma and τ = I α.

Start with a force diagram and remember that, when evaluating the torque, you must specify your axis of rotation. Note that this is also important for the moment of inertia!
I question the I = 1/2mr2. That is the moment of inertia of a solid cylinder or disc about its center of mass. Is the can hollow?

6. Mar 2, 2015

### Thynazgul

Yes the can is hollow, should I use mr2 instead? Anyways I believe static friction is something like μmg but how would I find the coefficient of friction? :(

7. Mar 2, 2015

### brainpushups

Yes. If the can is open on both ends. I would say that if it is only open on one end you should use the moment of inertia of the hollow cylinder (hollow can) PLUS the moment of inertia of the single end (solid disc). Perhaps you don't have all of the information for this... If so you'll be better off using the hollow cylinder formula.

No. Static friction is variable. It will always adjust itself to be equal and opposite to the force along the surface in the other direction. On FLAT ground the MAXIMUM force of static friction is μmg. Leave the force of friction as an unknown 'f.'