Rotational Motion on an Axis Problem: Helpppp?

In summary, it takes 2 seconds for the second sheet to reach the same angular velocity as the first sheet.
  • #1
cheechnchong
132
1
Rotational Motion on an Axis Problem: Helpppp?

Problem: Two thin rectangular sheets (0.20 m x 0.40 m) are identical. In the first sheet the axis of rotation lies along the 0.20-m side, and in the second it lies along the 0.40-m side. The same torque is applied to each sheet. The first sheet, starting from rest, reaches its final angular velocity in 8.0 s. How Long does it take for the second sheet, starting from rest, to reach teh same angular velocity?

My Approach: I Didn't setup any equations just yet...kinda confused about how to come up with the TIME!?? I drew the 2 identical rectangles on different axes (on on the 0.40-m side and the other on the 0.20-m side). From the given information, I know that both have equal torque and mass; however, radius I am not sure about since they're on different axis (should i use the moment of inertia I=mr^2 here? to figure the radius). Ok once i have the radius, WHERE do i plug it into find TIME!?

I think I know how to solve it, but it's just a few things i cannot figure from this problem. Thanks! :smile:
 
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  • #2
You should use I=mr2 to figure out what the moment of inertia is (well, something like that). Remember that T=I*a where T is torque, I moment of inertia and a angular acceleration. So figure out what their relative angular accelerations are, and from there you should be able to figure out how long it takes one to reach a certain angular velocity in relation with the other
 
  • #3
Office_Shredder said:
You should use I=mr2 to figure out what the moment of inertia is (well, something like that). Remember that T=I*a where T is torque, I moment of inertia and a angular acceleration. So figure out what their relative angular accelerations are, and from there you should be able to figure out how long it takes one to reach a certain angular velocity in relation with the other

How can i find the Torque without a GIVEN acceleration? and how can i utilize the angular velocities given at REST (w initial = 0 m/s). lol it's a hellva problem.
 
  • #4
I think, as office shredder says, it's about relative acceleration, Intertia and time. Doing it that way gave me 2s. Am I close?
 
  • #5
rsk said:
I think, as office shredder says, it's about relative acceleration, Intertia and time. Doing it that way gave me 2s. Am I close?

YOU ARE RIGHT ON THE MONEY! how did you do it--in steps? oh and is the I = 1/3mr^2 (since it's a rectangle)?
 
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  • #6
^^how in the world did you calculate that answer? my first question is...where did you get the first acceleration in order to find the torque shared by the two rectangles? because if i can get the torque i can set the other one equal to it and FIND the 2nd acceleration. From that acceleration i just don't know what else to do...?
 
  • #7
Ok, here we go. Let's start by getting the moment of inertia of each one.

I=m*r2 Clearly m is the same for both. Now, you should realize that by r in this problem, r is the distance from the axis of rotation to the center of mass of the object. So r is either .1, or .2 depending on the orientation. So if it rotates through the .4 meter side, I.4=m*.12, and if it rotates around the .2 meter side, I.2=m*.22

The important point is that I.4/I.2 = 1/4 (do you see how?)

To if the two torques are equivalent, we have T=Ia for both. So I.4*a.4 = I.2*a.2

So a.2/a.4 = 1/4

Assume both are rotating up to a final angular velocity V We know the general formula for the angular velocity given angular acceleration and time is:

v= a*t

if the initial angular momentum is zero. So we have V=a.4*t.4=a.2*t.2

Or

4 = t.2/t.4

But we know t.2 = 8, so t.4 = 8/4 = 2
 
  • #8
^^beautiful connections...i knew it some kinda tricky question! i woulda stayed up nights trying to figure this one out. Now i see that you carried this out as a proportional problem; therefore, next time i'll know what to look for. BIG THANKS!
 

Related to Rotational Motion on an Axis Problem: Helpppp?

What is rotational motion on an axis?

Rotational motion on an axis refers to the movement of an object around a fixed point or axis. This type of motion can occur in circular or curved paths.

What factors affect rotational motion on an axis?

The factors that affect rotational motion on an axis include the mass of the object, the distance from the axis of rotation, and the applied torque or force.

How is rotational motion on an axis different from linear motion?

Rotational motion on an axis involves the rotation of an object around an axis, while linear motion involves the movement of an object in a straight line. Additionally, rotational motion involves torque and rotational inertia, while linear motion involves force and mass.

What is the law of conservation of angular momentum?

The law of conservation of angular momentum states that the total angular momentum of a system remains constant unless an external torque is applied. This means that the angular momentum of a system cannot be created or destroyed, only transferred or transformed.

How can I solve problems involving rotational motion on an axis?

To solve problems involving rotational motion on an axis, you can use equations such as the rotational kinematic equations and the law of conservation of angular momentum. It is also important to understand the concepts of torque, rotational inertia, and angular velocity.

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