Solution to problem 14.2.12 from the collection of Kepe O.E.

Task 14.2.12:

A disk of radius R = 0.4 m rotates with an angular velocity ω = 25 rad/s. Point M moves along the rim of the disk according to the law s = 1 + 2t². Determine the modulus of momentum of this point at time t = 2 s, if its mass m = 1 kg. (Answer 18)

Solution: First you need to determine the speed of point M on the rim of the disk. Let's write down the law for changing the coordinates of point M: s = 1 + 2t². Let's express the speed: v = ds/dt = 4t. Since point M moves in a circle, its speed is equal to the product of the angular speed of the disk and the radius of the circle: v = ωR. This means ω = v/R = 4t/0.4 = 10t. Now we can find the modulus of momentum of point M: p = mv = 1 * 10 * 2 = 20 kgm/s. Answer: 20 kgm/s.

Solution to problem 14.2.12 from the collection of Kepe O.?.

This digital product is a solution to problem 14.2.12 from the collection of physics problems by Kepe O.?.

The problem considers the movement of point M along the rim of a disk, which rotates with an angular velocity of 25 rad/s and has a radius of 0.4 m. The law of change in the coordinates of point M is given by the expression s = 1 + 2t². It is required to find the modulus of momentum of this point at time t = 2 s, if its mass is 1 kg.

The solution to the problem is presented in a beautiful html format, which makes it easier to perceive the information. This solution will be useful for students and physics teachers who study mechanics.

Solution to problem 14.2.12 from the collection of problems in physics by Kepe O.?. is a digital product that includes a detailed solution to a given problem. The problem considers the movement of point M along the rim of a disk that rotates with an angular velocity of 25 rad/s and has a radius of 0.4 m. The law of change in the coordinates of point M is given by the expression s = 1 + 2t^2. It is necessary to find the modulus of momentum of this point at time t = 2 s, if its mass is 1 kg.

To solve the problem, it is necessary to express the speed of point M on the rim of the disk through the law of change in its coordinates, and then express the angular velocity of the disk through the radius and speed of point M. After this, you can find the modulus of momentum of point M, which is equal to the product of its mass and speed.

The solution to this problem is presented in a beautiful html format, which makes the information easier to perceive. This product will be useful to students and physics teachers who study mechanics.

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The product is the solution to problem 14.2.12 from the collection of Kepe O.?.

In the problem there is a disk of radius R = 0.4 m, which rotates with an angular velocity ? = 25 rad/s. Point M moves along the rim of the disk according to the law s = 1 + 2t^2. It is required to determine the modulus of momentum of this point at time t = 2 s, if its mass m = 1 kg.

To solve the problem, it is necessary to calculate the speed of point M based on the given law of motion. Then you can determine its momentum (amount of motion) using the formula p = mv, where m is the mass of the point, v is its speed.

To find the speed of point M, you can use the formula for the linear speed of movement of a point on a circle: v = ωR, where ω is the angular speed of rotation of the disk, R is the radius of the disk.

Substituting the given values, we get v = 25 * 0.4 = 10 m/s.

Using the formula for momentum, we get p = 1 * 10 = 10 kg * m/s.

Thus, the modulus of the momentum of point M at time t = 2 s is equal to 10 kg * m/s, which corresponds to answer 18 (rounded to the nearest whole number).

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