Rotational Motion Question, lever arm with two masses

I really appreciate your help!In summary, the question involves a uniform rigid rod with two point-like particles attached at the ends, rotating in the vertical xy plane. The goal is to find the magnitude of the angular acceleration when the rod is at an angle of 51.1 degrees with the horizontal. To solve this, the moment of inertia of the system must be calculated, as well as the gravitational forces and their components acting perpendicular to the lever arm. After calculating the net torque/moment and the moment of inertia, the angular acceleration can be determined. However, it is important to note that the moment of inertia for the system includes the inertias of both masses at the ends of the rod.
  • #1
shmoop

Homework Statement


[/B]
A uniform rigid rod with mass Mr = 2.7 kg, length L = 3.1 m rotates in the vertical xy plane about a frictionless pivot through its center. Two point-like particles m1 and m2, with masses m1 = 6.7 kg and m2 = 1.6 kg, are attached at the ends of the rod. What is the magnitude of the angular acceleration of the system when the rod makes an angle of 51.1 degrees with the horizontal? (m2 is 51.1 degrees above the horizontal, and m1 is 51.1 degrees below the horizontal).

Homework Equations



Torque=Inertia*Angular Acceleration

Inertia of uniform rigid rod = mL^2/12

The Attempt at a Solution



I began by calculating inertia, like this:

I = mL^2/12 = (2.7kg)(3.1m)2/12=2.16225 kgm2

Then I calculated the gravitational forces from m1 and m2:

m1g=(6.7kg)(9.8m/s2)=65.66N

m2g=(1.6kg)(9.8m/s2)=15.68N

Then I determined the component of these forces which act perpendicular to the lever arm:

65.66N*cos51.1=41.23N

15.68N*cos51.1=9.84N

Then I calculated the net torque/moment (clockwise negative, counterclockwise positive):

Radius = 1/2(3.1m)=1.55m

Torque = (1.55m41.23N)-(1.55m9.84N) = 48.65Nm

Then I calculated the angular acceleration:

Angular acceleration = Torque/Inertia

Angular acceleration = 48.65Nm/2.16kg*m2

Angular acceleration = 22.52 rad/s2

I have been told my answer is incorrect through an online system where I am able to check my answers, however I'm not sure where I went wrong. If anyone would be able to spot an error, or guide me in the right direction, it would be greatly appreciated!
 
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  • #2
Hi shmoop,

Welcome to Physics Forums!

Take another look at your moment of inertia for the system. What masses will contribute to the moment of inertia?
 
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Likes shmoop and scottdave
  • #3
gneill said:
Hi shmoop,

Welcome to Physics Forums!

Take another look at your moment of inertia for the system. What masses will contribute to the moment of inertia?

Thank you SO much! I figured it out by adding the inertias of the two masses at the ends to the total inertia.
 

Related to Rotational Motion Question, lever arm with two masses

1. What is rotational motion and how is it different from linear motion?

Rotational motion is the movement of an object around an axis or center point. It is different from linear motion because the object moves in a circular path rather than a straight line.

2. What is a lever arm and how is it related to rotational motion?

A lever arm is the distance between the axis of rotation and a force acting on an object. It is related to rotational motion because it determines the torque, or rotational force, on an object.

3. How do you calculate the lever arm of a system with two masses?

The lever arm can be calculated by finding the perpendicular distance from the axis of rotation to the line of action of the force for each mass, and then adding these distances together.

4. How does the distribution of masses affect the lever arm and rotational motion?

The distribution of masses affects the lever arm because it determines the distance of each mass from the axis of rotation. This, in turn, affects the torque and rotational motion of the system.

5. What are some real-world examples of rotational motion and lever arms?

Some examples of rotational motion and lever arms include the motion of a pendulum, the rotation of a bicycle wheel, and the movement of a see-saw. In each of these examples, the object rotates around an axis and the lever arm plays a role in the motion of the system.

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