# Solving for Net Torque on Uniform Mass Density Rod

• taloz
In summary: Since we know the initial angular velocity, \omega0, and the final angular velocity is 0, we can solve for t, which will give us the time it takes for the rod to come to rest.Finally, we can use the formula for the number of revolutions, N = \omega * t / 2\pi, to calculate the number of revolutions the rod makes before coming to rest.In summary, to solve this problem, you need to understand the concepts of moment of inertia, angular velocity, torque, and angular acceleration. By using the given values and the relevant formulas, you can solve for the radius, angular velocity, and angular acceleration, and ultimately find the number of revolutions the rod makes before coming to rest
taloz

## Homework Statement

A rod has a uniform mass density of 0.05 kg/cm it has a moment of inertia equal to 0.1ML^2. The rod sweeps out an area equal to 0.25* pi meters squared in 4 seconds. If you apply a net torque of -1/16 Nm to the rotating rod, how many revolutions will the rod make before coming to rest.As i don't have a scanner on me i'll do my best to describe the rod. It's rotating about it's center in a counterclockwise direction. Therefore the -1/16 Nm should slow it down.

## Homework Equations

Torque = I*Angular Acceleration

I=0.1 *M* L^2

$$\omega$$ = V/r

## The Attempt at a Solution

Okay, i know that if the rod sweeps out an area equal to 0.25 * $$\pi$$ in 4 seconds, that each rod is sweeping an area of half of that. Therefore, the linear velocity of the system right before the application of torque is (1/32) * $$\pi$$ m/s.

I know that i have to solve for the radius of the rod now if order to convert linear velocity into angular velocity, and to solve for the moment of inertia so that i can find the angular acceleration. However, my teacher has never given us a problem with uniform mass density before, so i don't understand how to use it in order to solve for this radius.

If anyone can help that would be great :)

Last edited:

Hi there! I would approach this problem by first understanding the concept of moment of inertia and how it relates to the distribution of mass in an object. In this case, the rod has a uniform mass density, which means that the mass is evenly distributed along the length of the rod.

To solve for the radius, you can use the formula for moment of inertia, I = mr^2, where m is the mass and r is the radius. Since the rod has a uniform mass density, you can rewrite the formula as I = (mass density * length) * r^2.

Now, we can plug in the given values to solve for r. We know that the mass density is 0.05 kg/cm, and the length of the rod is not given, so we can use a variable, L, to represent it. Therefore, our formula becomes I = 0.05 * L * r^2.

Next, we can plug in the given value for the moment of inertia, 0.1ML^2, and solve for r. This gives us 0.1ML^2 = 0.05 * L * r^2. Simplifying, we get r = sqrt(0.2L).

Now that we have the radius, we can use the angular velocity formula, \omega = V/r, to solve for the angular velocity, which is equal to the linear velocity divided by the radius. Plugging in the given value for linear velocity, (1/32) * \pi m/s, and the calculated value for r, sqrt(0.2L), we get \omega = (1/32) * \pi / sqrt(0.2L).

Finally, we can use the torque formula, Torque = I * Angular Acceleration, to solve for the angular acceleration. Plugging in the given value for torque, -1/16 Nm, and the calculated value for moment of inertia, 0.1 * M * L^2, we get -1/16 = (0.1 * M * L^2) * Angular Acceleration.

Now, we can solve for the angular acceleration, which will give us the rate at which the rod is slowing down. Once we have this, we can use the formula for angular velocity, \omega = \omega0 + \alpha * t, to find the final angular velocity at the point when the rod comes to

## What is net torque on a uniform mass density rod?

The net torque on a uniform mass density rod is the measure of the rotational force applied to the rod. It is calculated by multiplying the force applied to the rod by the distance from the point of rotation to the point of force application.

## What is the formula for calculating net torque on a uniform mass density rod?

The formula for calculating net torque on a uniform mass density rod is T = F x d, where T is the torque, F is the force applied to the rod, and d is the distance from the point of rotation to the point of force application.

## How do you find the direction of net torque on a uniform mass density rod?

The direction of net torque on a uniform mass density rod can be found using the right-hand rule. Point your right thumb in the direction of the force applied to the rod and your fingers will curl in the direction of the net torque.

## What factors affect the net torque on a uniform mass density rod?

The net torque on a uniform mass density rod is affected by the magnitude and direction of the force applied to the rod, as well as the distance from the point of rotation to the point of force application. The shape and mass distribution of the rod also play a role in determining the net torque.

## How is net torque used in real-world applications?

Net torque is an important concept in many real-world applications, such as engineering and physics. It is used to understand and predict the rotational motion of objects, such as the movement of gears in a machine or the motion of a spinning top. It is also used in designing structures, such as bridges and buildings, to ensure they can withstand the forces of rotation.

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