# Classical mechanics-acc. of a rod using inertia

• indie452
Then, use this value to find the angular acceleration by dividing the torque by the moment of inertia. The initial acceleration of the free end is found to be 3g/2 when one person lets go. In summary, to find the initial acceleration of the free end when one person lets go of a rod of length l and mass M, use the parallel axis theorem to find the moment of inertia about the pivot point and then divide the torque by the moment of inertia. The resulting acceleration is 3g/2.
indie452

## 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

## 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?

Calculate the moment of inertia about the pivot point using the parallel axis theorem.

I would suggest that you double check your calculations and make sure you are using the correct equations for rotational motion. In this scenario, the rod is being released at one end, which means the other end is rotating about a fixed point (the other person's hand). This requires the use of angular velocity and angular acceleration, instead of linear velocity and linear acceleration. Additionally, make sure you are using the correct values for the moment of inertia, which may differ depending on the axis of rotation.

Furthermore, it is important to consider the forces acting on the rod, such as the force of gravity and the force exerted by the person holding the other end. These forces may affect the acceleration of the free end of the rod and should be taken into account in your calculations.

I would also suggest breaking down the problem into smaller, simpler steps and using diagrams to visualize the situation. This can help in identifying any errors and understanding the concept better.

Overall, it is important to carefully analyze the problem and use the correct equations and values in order to arrive at the correct solution.

## What is classical mechanics?

Classical mechanics is a branch of physics that studies the motion of objects under the influence of forces. It is based on Newton's laws of motion and the concept of inertia.

## What is the acceleration of a rod using inertia?

The acceleration of a rod using inertia refers to the rate of change of its velocity due to the forces acting on it. Inertia is the tendency of an object to resist changes in its motion, so the acceleration of a rod using inertia depends on the magnitude and direction of the forces acting on it.

## How is the acceleration of a rod affected by its mass?

According to Newton's second law of motion, the acceleration of a rod is directly proportional to the net force acting on it and inversely proportional to its mass. This means that a heavier rod will have a smaller acceleration than a lighter rod when the same force is applied.

## What is the difference between linear and angular acceleration?

Linear acceleration refers to the change in an object's linear velocity, while angular acceleration refers to the change in its angular velocity. Linear acceleration is measured in meters per second squared, while angular acceleration is measured in radians per second squared.

## What are the applications of classical mechanics in everyday life?

Classical mechanics has many practical applications, including the design of structures and machines, the study of the motion of planets and other celestial bodies, and the development of technologies such as cars and airplanes. It also helps us understand the behavior of everyday objects, such as balls rolling down a hill or a pendulum swinging back and forth.

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