Find angular acceleration using theoretical values

AI Thread Summary
The discussion focuses on calculating the angular acceleration of a rolling tin can using theoretical values, with participants exploring various equations and methods. Key equations include the relationship between linear and angular velocity, torque, and moment of inertia, with specific attention to whether the can is solid or hollow. The importance of understanding the role of friction in torque calculations is emphasized, as well as the need to clarify the conditions of the experiment, such as whether the can rolls down an incline. Participants suggest using a force diagram and acknowledge that static friction is variable, complicating the calculations. Ultimately, the conversation highlights the necessity of determining the correct moment of inertia based on the can's structure and the unknowns involved in the frictional forces.
Thynazgul
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Homework Statement


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.

Homework Equations


v= angular velocity * radius
acceleration = torque / moment of inertia
moment of inertia = 1/2mr2
v= square root (gh)
angular acceleration = change in angular velocity / change in time
Torque = force * radius

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.
 
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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.
 
brainpushups said:
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.
Exaclty, sorry I forgot to mention that.
 
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...
 
Thynazgul said:
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.

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?
 
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? :(
 
Thynazgul said:
Yes the can is hollow, should I use mr2 instead?

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.

Thynazgul said:
I believe static friction is something like μmg
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.'
 
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