Question

12. Маховик в виде сплошного диска, момент инерции которого J, вращаясь при торможении равнозамедленно, за время t уменьшило частоту с ω1 до ω2. Определите работу силы торможения.

Answer 1

Работа по торможению равна разности кинетической энергии в начале и конце торможения A=J*(w2^2-w1^2)/2

Answer 2

Calculation of Work Done by the Braking Force

To determine the work done by the braking force on the solid disk flywheel, we need to consider the change in angular velocity and the moment of inertia of the flywheel.

Let's denote the initial angular velocity as ω1 and the final angular velocity as ω2. The moment of inertia of the flywheel is represented by J.

The work done by a force is given by the formula:

Work = Force × Distance

In rotational motion, the work done by a torque is given by:

Work = Torque × Angle

Since the braking force acts tangentially on the flywheel, it produces a torque that opposes the rotational motion. The torque is given by:

Torque = Moment of Inertia × Angular Acceleration

In this case, the angular acceleration is constant because the flywheel is slowing down uniformly. Therefore, we can use the equation:

Angular Acceleration = (Change in Angular Velocity) / Time

Substituting the values into the equation, we have:

Torque = J × ((ω2 - ω1) / t)

Now, we can calculate the work done by the braking force:

Work = Torque × Angle

Since the braking force slows down the flywheel uniformly, the angle through which the torque acts is given by:

Angle = (Change in Angular Velocity) × Time

Substituting the values into the equation, we have:

Angle = (ω2 - ω1) × t

Finally, we can calculate the work done by the braking force:

Work = (J × ((ω2 - ω1) / t)) × ((ω2 - ω1) × t)

Simplifying the equation, we get:

Work = J × (ω2 - ω1)^2

Therefore, the work done by the braking force on the solid disk flywheel is J × (ω2 - ω1)^2.

Please note that the specific values of J, ω1, ω2, and t are not provided in the question, so we cannot calculate the exact numerical value of the work done without this information.