# Classical mechanics-acc. of a rod using inertia

• indie452
In summary, the problem involves two people holding opposite ends of a rod with length l and mass M. It is required to show that when one person lets go, the initial acceleration of the free end is 3g/2. The solution involves calculating the moment of inertia about the pivot point instead of the center of the rod, and using torque to find the answer. The next part of the question involves showing how the load supported by the one person falls from mg/2 to mg/4, which requires considering the balance of downward and upward forces.
indie452
1. Homework Statement

two people are holding the ends of a rod length l and mass M, show that if one person let's go the initial acceleration of the free end is 3g/2

3. The Attempt at a Solution
i worked out the moment of inertia about centre mass (cm) and got = Ml2/12

because L=Iw
dL/dt = I*dw/dt
torque (T) = I*ang.acc. (a)
so
a = T/I = mglsin[90] / Ml2/12
= 12g/l
this is wrong so i used l=l/2 as this is the distance to the cm.
so a = 24g/l also wrong

what am i doing wrong?

indie452 said:
1. Homework Statement

two people are holding the ends of a rod length l and mass M, show that if one person let's go the initial acceleration of the free end is 3g/2

3. The Attempt at a Solution
i worked out the moment of inertia about centre mass (cm) and got = Ml2/12

Are you sure? As you state, this is the moment of inertia about the center of the rod. But if two people are holding the ends and one let's go, it is not rotating about the center, is it?

yeah i realized that now and took the mom.of inertia at the pivot and with torqu found the answer.

the next part of the question however is show how the load supported by the one person falls from mg/2 to mg/4.

i have thought about balancing out the downward forces and the upward forces

F1=mg/2 ...F2=mg/2
^......^
|__________________|
....|
....V
.....F=mg

but for the next part after one person has let go i tried saying that F2 will become a downward force = 3mg/2 but this doesn't seem right

## 1. What is classical mechanics?

Classical mechanics is a branch of physics that deals with the motion of macroscopic objects, such as particles, bodies, and systems of particles. It is based on Newton's laws of motion and the concept of inertia.

## 2. How is the acceleration of a rod determined using inertia?

The acceleration of a rod can be determined using the principle of inertia, which states that an object at rest will remain at rest or an object in motion will continue in motion at a constant velocity unless acted upon by an external force. In the case of a rod, the external force may be gravity or a force applied at one end of the rod, and the acceleration can be calculated using Newton's second law of motion.

## 3. What factors affect the acceleration of a rod?

The acceleration of a rod can be affected by several factors, including the mass and shape of the rod, the force being applied to the rod, and any external forces acting on the rod, such as friction or air resistance.

## 4. How is classical mechanics different from quantum mechanics?

Classical mechanics deals with the motion of macroscopic objects, while quantum mechanics deals with the behavior of subatomic particles. Classical mechanics is based on Newton's laws of motion, while quantum mechanics is based on the principles of wave-particle duality and uncertainty.

## 5. What are some real-world applications of classical mechanics?

Classical mechanics has many real-world applications, including the design and analysis of structures and machines, the study of planetary motion and celestial mechanics, and the development of technologies such as cars, airplanes, and rockets. It is also essential for understanding and predicting the behavior of everyday objects and phenomena.

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