Solution to problem 15.5.3 from the collection of Kepe O.E.

15.5.3 It is necessary to calculate the kinetic energy of a system consisting of two identical gears weighing 1 kg each. The wheels rotate at an angular speed of 10 rad/s. The radius of inertia of each wheel relative to the axis of rotation is 0.2 m. The answer is the number 4.

To solve this problem, you need to use the formula to calculate the kinetic energy of a rotating body:

E = (I * w^2) / 2

where E is kinetic energy, I is moment of inertia, w is angular velocity.

For each wheel, the moment of inertia can be calculated using the formula:

I = (m * r^2) / 2

where m is the mass of the wheel, r is the radius of gyration.

Substituting the data from the problem statement, we get:

I = (1 kg * 0.2 m)^2 / 2 = 0.02 kg * m^2

E = 2 * (0.02 kg * m^2) * (10 rad/s)^2 / 2 = 4 J

Answer: 4.

Solution to problem 15.5.3 from the collection of Kepe O.?.

We present to your attention a unique digital product - the solution to problem 15.5.3 from the collection of Kepe O.?. This problem solves the problem of calculating the kinetic energy of a system consisting of two identical gears weighing 1 kg each, rotating at an angular velocity of 10 rad/s. The radius of inertia of each wheel relative to the axis of rotation is 0.2 m.

Our solution contains a detailed description of all calculations and formulas used to obtain the result. You can easily understand each step of the solution and check if it is correct.

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• Price: 99 rubles

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Solution to problem 15.5.3 from the collection of Kepe O.?. consists in determining the kinetic energy of a system consisting of two identical gears weighing 1 kg each, which rotate with an angular velocity of 10 rad/s. The radius of inertia of each wheel relative to the axis of rotation is 0.2 m.

To solve this problem, it is necessary to calculate the moment of inertia of each wheel relative to its axis of rotation, using the formula I = mr^2, where m is the mass of the wheel, r is the radius of inertia of the wheel. Then you need to find the moment of inertia of the system using the formula I = I1 + I2, where I1 and I2 are the moments of inertia of each wheel.

After this, it is necessary to calculate the kinetic energy of the system using the formula K = (1/2)I?^2, where ? - angular velocity of the system.

So, substituting the known values, we get:

I = mr^2 = 1 * 0.2^2 = 0.04 kg*m^2

Isystem = I1 + I2 = 0.04 + 0.04 = 0.08 kg*m^2

K = (1/2)I?^2 = (1/2) * 0.08 * 10^2 = 4 J

Answer: 4 J.

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