Angular acceleration problem - masses on massless rod

In summary, the conversation discusses the calculation of angular acceleration for a system consisting of a 3 kg mass and a 4 kg mass attached to either end of a 3 m long massless rod. The question is posed about the size of the angular acceleration when the system is rotated about the center of mass by a force of 7 N acting on the 4 kg mass. The individual uses the equation rF/mr^2 to calculate the angular acceleration, but receives an incorrect answer. It is then suggested to first find the center of mass and use the moment of inertia in the calculation. After some discussion, the individual realizes their mistake and thanks the other person for their help.
  • #1
FlipStyle1308
267
0
A 3 kg mass and a 4 kg mass are attached to either end of a 3 m long massless rod. If the system is rotated about the center of mass by a force of 7 N acting on the 4 kg mass, (perpendicular to the rod), what will the size of the angular acceleration of the system be?

I used angular acceleration = rF/mr^2, and got 1.3608 rad/s^2, but got the answer wrong. Anyone have any idea why?
 
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  • #2
FlipStyle1308 said:
A 3 kg mass and a 4 kg mass are attached to either end of a 3 m long massless rod. If the system is rotated about the center of mass by a force of 7 N acting on the 4 kg mass, (perpendicular to the rod), what will the size of the angular acceleration of the system be?

I used angular acceleration = rF/mr^2, and got 1.3608 rad/s^2, but got the answer wrong. Anyone have any idea why?

What did you use for r? You must first find where the center of mass is. Did you do this?
 
  • #3
For r I used 1.286. I got the center of mass is 15.4286 kgm^2, which is correct, according to WebAssign.
 
  • #4
FlipStyle1308 said:
For r I used 1.286. I got the center of mass is 15.4286 kgm^2, which is correct, according to WebAssign.

Ok (btw, the value you give is the moment of inertia, not the center of mass).

I think you just made a mistake using your calculator. I used your values and got a different alpha (0.5835 rad/s^2)
 
  • #5
Whoops, you're right, I gave the rotational inertia for the center of the rod lol. Center of mass is 1.714 m, from the 3 kg mass. What did you plug in for that 0.5835?
 
  • #6
FlipStyle1308 said:
Whoops, you're right, I gave the rotational inertia for the center of the rod lol. Center of mass is 1.714 m, from the 3 kg mass. What did you plug in for that 0.5835?

rF/I = 1.286m * 7 N/15.428 kg m^2
 
  • #7
Oh okay, thanks! So I was supposed to use the inertia of the center of mass. Interesting. Thanks!
 
  • #8
FlipStyle1308 said:
Oh okay, thanks! So I was supposed to use the inertia of the center of mass. Interesting. Thanks!
I am not sure what you mean. But the r you use there is the distance between where the force is applied and the axis of rotation, as a general principle. And the I is always calculated with respect to where the axis of rotation is located.
 
  • #9
Makes sense...I never thought of that. Thanks!
 

1. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity. It is a measure of how quickly an object is rotating or changing its rotational speed.

2. How is angular acceleration different from linear acceleration?

Angular acceleration is a measure of change in rotational motion, while linear acceleration is a measure of change in linear motion. Angular acceleration is expressed in units of radians per second squared, while linear acceleration is expressed in units of meters per second squared.

3. What is the formula for calculating angular acceleration?

The formula for angular acceleration is α = (ωf - ωi) / t, where α is angular acceleration, ωf is final angular velocity, ωi is initial angular velocity, and t is the time interval.

4. How do masses on a massless rod affect the angular acceleration?

In a system with masses on a massless rod, the angular acceleration is affected by the distribution of the masses along the rod. The further the masses are from the axis of rotation, the greater the moment of inertia and the slower the angular acceleration will be.

5. What are some real-life examples of angular acceleration problems with masses on a massless rod?

One example is a balance scale with two equal masses placed at different distances from the pivot point. Another example is a spinning top with different masses placed at different distances from the axis of rotation. These systems demonstrate how the distribution of mass affects the angular acceleration.

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