Solution of problem D3 (task 2) Option 06 Dievsky V.A.

As part of task 2 on the topic "THEOREM ABOUT CHANGE OF KINETIC ENERGY" in mechanical systems shown in diagrams 1-30, it is necessary to determine the angular velocity (options 4, 6, 7, 9, 11, 18, 25, 26, 28) or linear speed (other options) of body 1 after its given movement Fi1 = 2pi rad or S1 = 2 m. All systems are at rest at the initial moment of time.

Let's consider the solution to problem 2 for scheme No. 6. To do this, we will use the theorem on the change in kinetic energy in integral form.

The diagram shows a disk of radius R located on a horizontal plane. Body 1 is a point located at a distance R/2 from the center of the disk. Body 2 is a point located at a distance R from the center of the disk and connected to it by a weightless rod structure.

When a disk rotates with an angular velocity w, its kinetic energy is expressed as T = I*w^2/2, where I is the moment of inertia of the disk relative to its center of mass.

At the initial moment of time, the disk is at rest, therefore, its kinetic energy is zero: T1 = 0. After rotation through an angle Phi1 = 2pi rad, its kinetic energy becomes equal to:

T2 = Iw^2/2 = (mR^2/2)w^2/2 = mR^2*w^2/4,

where m is the mass of the disk.

According to the theorem on the change in kinetic energy in integral form, the change in the kinetic energy of a system during movement is equal to the work of all external forces acting on the system. In this case, there are no external forces, therefore, the change in kinetic energy is zero:

T2 - T1 = 0.

It follows that the angular velocity of the disk after rotation through the angle Phi1 = 2pi rad is equal to zero: w = 0.

Thus, the answer to task 2 for scheme No. 6 is that the angular velocity of the disk after rotation through the angle Phi1 = 2pi rad is equal to zero.

Solution of problem D3 (task 2) Option 06 Dievsky V.A.

This solution is an answer to task 2 on the topic “THEOREM ABOUT CHANGE OF KINETIC ENERGY” in mechanical systems given in the textbook by V.A. Dievsky. In the task it is necessary to determine the angular velocity of body 1 after a given displacement Fi1 = 2pi rad. Solution option - 06.

The solution is made using the theorem on the change in kinetic energy in integral form. All information is presented in an easily understandable form and can be used to independently study the topic.

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solution to task 2 in theoretical mechanics D3 (dynamics problem 3) on the topic “Theorem on the change in kinetic energy” for option 6, scheme No. 6 from the collection of tasks “Theoretical mechanics” Dievsky V.A., Malysheva I.A. 2009 for university students. The solution is made in Word format (handwritten solution or typed in Word) and packed in a zip archive that will open on any PC. The task involves determining the angular velocity of body 1 after a given displacement Fi1 = 2π rad or S1 = 2 m, using the theorem on the change in kinetic energy in integral form. Movement begins from a state of rest. After paying for the goods, you will receive a link to the archive with the solution to the task. After checking the solution, the author will be grateful if you leave positive feedback.

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