# Solve Acceleration of Rod's Centre of Mass

• Diganta28
In summary, the problem involves a rod of length l on a frictionless surface being disturbed and asked to find the acceleration of its center of mass. The equations used include acceleration formula, torque formula, and force formula. The attempt at a solution involved setting up equations and solving, but the given answer is different.
Diganta28
1. Homework Statement :

A rod of length l is vertically standing on a friction less surface.
It is slightly disturbed from this position. Let w(omega) and alpha be the angular speed and angular acceleration of the rod, when it turns through an angle theta, then find the value of acceleration of centre of mass of the rod.

2. Homework Equations :

acom = ( Fnet/mnet)

tau = i * alpha

tau= force*perpendicular distance from axis of rotation

3. The Attempt at a Solution :

Tried like this (but no luck):

(mg-N)=ma , where a is the required answer.N * (l/2) sin theta = (1/12 m (l)^2) * alpha

Solved to get : a = g-(l * alpha/(6 sin theta)).

l *(alpha/2)* sin theta + (w^2*l/2) cos theta

Ok I understood what they are doing.

g - (l*alpha/(6 sin theta)) wrong?

## 1. What is the formula for calculating the acceleration of a rod's center of mass?

The formula for calculating the acceleration of a rod's center of mass is: a = α * L/2, where a is the acceleration, α is the angular acceleration, and L is the length of the rod.

## 2. How do I determine the direction of the acceleration of a rod's center of mass?

The direction of the acceleration of a rod's center of mass is determined by the direction of the angular acceleration. If the rod is rotating clockwise, the acceleration of its center of mass will be in the opposite direction, and if the rod is rotating counterclockwise, the acceleration of its center of mass will be in the same direction.

## 3. Can the acceleration of a rod's center of mass be negative?

Yes, the acceleration of a rod's center of mass can be negative. This indicates that the rod is decelerating or slowing down.

## 4. How does the mass distribution of a rod affect its acceleration?

The mass distribution of a rod can affect its acceleration by changing the moment of inertia, which is a measure of how difficult it is to rotate an object. A rod with more mass concentrated towards its ends will have a larger moment of inertia and thus a smaller acceleration compared to a rod with the same mass distributed evenly.

## 5. Can the acceleration of a rod's center of mass change over time?

Yes, the acceleration of a rod's center of mass can change over time if the angular acceleration changes. This can happen if an external force is applied to the rod or if the mass distribution is altered. The acceleration can also change if the rod is in a non-uniform gravitational field.

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