Solution to problem 9.3.3 from the collection of Kepe O.E.

9.3.3 The wheel moves according to the equations xc = 2t2, yc = 0.5 m. It is necessary to find the angular acceleration of the wheel. Answer: 8.

To solve this problem, it is necessary to use the formula for determining the angular acceleration: α = a / r, where α is the angular acceleration, a is the linear acceleration, r is the radius of the wheel.

From the equation xc = 2t2, one can determine the linear acceleration a = 4 m/s² (second derivative with respect to time). The wheel radius is not specified, so its value must be known or guessed.

Substituting the known values ​​into the formula, we get: α = 4 / r. To find the angular acceleration value, you need to know the radius of the wheel.

The answer to the problem depends on the value of the wheel radius and is equal to 4 / r in rad/c². If, for example, the radius of the wheel is 0.5 meters, then the angular acceleration is 8 rad/s².

Solution to problem 9.3.3 from the collection of Kepe O.?. is a digital product designed for those studying mathematics and physics. This product is a detailed solution to a problem that appears in the collection of Kepe O.?. and is associated with the movement of the wheel.

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We offer a digital product “Solution to problem 9.3.3 from the collection of Kepe O.?”, which contains a detailed solution to the problem related to the movement of a wheel. In order to find the angular acceleration of the wheel using the given equations, it is necessary to use the formula α = a / r, where α is the angular acceleration, a is the linear acceleration, r is the radius of the wheel. From the equation xc = 2t2, one can determine the linear acceleration a = 4 m/s² (second derivative with respect to time). The wheel radius is not specified, so its value must be known or guessed. Substituting the known values ​​into the formula, we get: α = 4 / r. The answer to the problem depends on the value of the wheel radius and is equal to 4 / r in rad/c². If, for example, the radius of the wheel is 0.5 meters, then the angular acceleration is 8 rad/s².

The digital product is designed using beautiful HTML elements that make its presentation more attractive and easier to read. This product is intended for those who study mathematics and physics, and can be used as material for preparing for exams or to expand knowledge in these areas. In addition, this product is environmentally friendly, as it does not require the use of paper and other materials for its production and storage.

Digital product "Solution to problem 9.3.3 from the collection of Kepe O.?." represents a detailed solution to the problem of the movement of a wheel, which appears in the collection of Kepe O.?. Using the equations of motion of the wheel, xc = 2t2 and yc = 0.5 m, it is necessary to find the angular acceleration of the wheel. To solve the problem, it is necessary to use the formula α = a / r, where α is the angular acceleration, a is the linear acceleration, r is the radius of the wheel. From the equation xc = 2t2, one can determine the linear acceleration a = 4 m/s² (second derivative with respect to time). The wheel radius is not specified, so its value must be known or guessed. Substituting the known values ​​into the formula, we get: α = 4 / r. The answer to the problem depends on the value of the wheel radius and is equal to 4 / r in rad/c². For example, if the radius of the wheel is 0.5 meters, then the angular acceleration is 8 rad/s². The solution to the problem is designed using beautiful HTML elements, which makes its presentation more attractive and easier to read. By purchasing this digital product, you get access to the solution to Problem 9.3.3 in a format convenient for you. You can use it to prepare for exams or to expand your knowledge in mathematics and physics. In addition, this product is environmentally friendly, as it does not require the use of paper and other materials for its production and storage.

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Problem 9.3.3 from the collection of Kepe O.?. consists in determining the angular acceleration of a wheel that rolls in a straight line according to the law of motion xc = 2t2 and has a radius r = 0.5 m.

To solve the problem, it is necessary to use the formula for the connection between the linear and angular movements of the wheel:

v = ωr,

where v is the linear speed of a point on the wheel located at a distance r from its axis of rotation, ω is the angular speed of the wheel, r is the radius of the wheel.

We also use the formula for linear acceleration:

a = dv/dt,

where a is linear acceleration.

According to the conditions of the problem, the law of motion of the wheel has the form:

x(t) = 2t^2.

From this law we can express speed:

v(t) = dx/dt = 4t.

Now you can express the angular speed of the wheel by substituting the value of the linear speed and radius of the wheel into the formula:

ω = v/r = 4t/0.5 = 8t.

Next, let's express the linear acceleration:

a = dv/dt = 4.

Finally, we express the angular acceleration of the wheel using the formula for the relationship between linear and angular acceleration:

a = αr,

where α is the angular acceleration.

Thus we get:

α = a/r = 4/0.5 = 8 rad/s^2.

Answer: the angular acceleration of the wheel is 8 rad/s^2.

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