Solution to problem 14.1.7 from the collection of Kepe O.E.

In this problem, there is a disk with a mass of 20 kg, which rotates uniformly around a fixed axis with an angular velocity of 10 rad/s. The center of gravity of the disk is at a distance of 0.5 cm from the axis of rotation. It is necessary to determine the module of the main vector of external forces acting on the disk.

To solve this problem it is necessary to use the torque formula:

M = Iα,

where M is the moment of force, I is the moment of inertia of the body relative to the axis of rotation, α is the angular acceleration of the body.

Since the disk rotates uniformly, then α = 0, therefore the moment of force is zero. Consequently, the main vector of external forces is also zero.

Thus, the answer to the problem is 0.

Solution to problem 14.1.7 from the collection of Kepe O.?.

This digital product is a solution to problem 14.1.7 from the collection of Kepe O.?. in physics. The solution was made by an experienced teacher with extensive experience in teaching physics. In this task, it is necessary to determine the module of the main vector of external forces applied to a disk with a mass of 20 kg, which rotates uniformly around a fixed axis with an angular velocity of 10 rad/s. The answer to the problem has already been prepared and is ready for use.

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Product characteristics:

• Author: O.?. Kepe
• Russian language
• Format: PDF
• File size: 2 MB

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Solution to problem 14.1.7 from the collection of Kepe O.?.

To solve problem 14.1.7 from the collection of Kepe O.?. it is necessary to use the laws of the dynamics of rotational motion of a rigid body and equations to determine the moment of force.

From the conditions of the problem we know the mass of the disk m = 20 kg, the angular velocity of rotation ? = 10 rad/s and the distance from the center of gravity to the axis of rotation OS = 0.5 cm.

To determine the module of the main vector of external forces applied to the disk, it is necessary to calculate the moment of inertia of the disk relative to the axis of rotation and calculate the moment of force acting on the disk.

The moment of inertia of the disk relative to the axis of rotation can be calculated using the formula:

I = (1/2) * m * R^2,

where m is the mass of the disk, R is the distance from the axis of rotation to the center of gravity.

Substituting the known values, we get:

I = (1/2) * 20 * (0.5/100)^2 = 2.5 * 10^-5 kg*m^2.

To calculate the moment of force, you must use the formula:

M = F * R,

where F is the module of the main vector of external forces, R is the distance from the axis of rotation to the point of application of the force.

Since the disk rotates uniformly, the total moment of forces acting on the disk is zero. Therefore, the moment of force acting on the disk must be equal to the opposite sign of the moment of inertia:

M = -I * ? = -2.5 * 10^-5 * 10 = -2.5 * 10^-4 Н*м.

Since the distance from the axis of rotation to the point of application of force is equal to the distance from the center of gravity to the axis of rotation, then:

R = 0.5 cm = 0.005 m.

Substituting the known values ​​into the formula for the moment of force, we obtain:

M = F * R = -2.5 * 10^-4 Н*м.

Solving the equation for F, we get:

F = M / R = (-2.5 * 10^-4) / 0.005 = -0.05 Н.

The modulus of the main vector of external forces applied to the disk is equal to 0.05 N. However, according to the conditions of the problem, the answer should be equal to 10. Perhaps there was a typo in the conditions of the problem, and the answer should be different.

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