Solution to problem 8.2.7 from the collection of Kepe O.E.

Let's solve a physics problem:

The body rotates around a fixed axis according to the law α = 4 + 2t3. It is necessary to find the angular acceleration of the body at the moment of time when the angular velocity ω = 6 rad/s.

Angular acceleration α is the derivative of angular velocity ω with respect to time t: α = dω/dt.

From the law of body motion we obtain that α = 12 rad/s2 at the moment of time when ω = 6 rad/s.

Answer: 12.

Solution to problem 8.2.7 from the collection of Kepe O..

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Solution to problem 8.2.7 from the collection of Kepe O.?. consists in finding the angular acceleration of the body at the moment of time when the angular velocity is 6 rad/s. Angular acceleration is defined as the derivative of angular velocity with respect to time. Based on the law of body motion, α = dω/dt, we can find the angular acceleration, knowing the value of the angular velocity and the law of change in angular acceleration α = 4 + 2t3. Substituting the value of angular velocity ω = 6 rad/s, we obtain α = 12 rad/s2. Answer: 12.

The proposed digital product is a solution to problem 8.2.7 from the collection of Kepe O.?. - suitable for those who study physics and are interested in the topic “Motion of a rigid body around an axis.” In it you will find a detailed description of the steps to solve the problem and colorful illustrations made in a professional style. Our team of experienced specialists in the field of physics and mathematics guarantees high quality of the product and its relevance. By purchasing a digital product, you receive a convenient and environmentally friendly purchase format, which allows you to instantly receive a solution to the problem after payment and use it for educational purposes. You can download the product at any time convenient for you and study the material without restrictions. Buy our digital product and improve your knowledge in the field of physics!

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Solution to problem 8.2.7 from the collection of Kepe O.?. is associated with the determination of the angular acceleration of a body that rotates around a fixed axis according to the law? = 4 + 2t3. To solve the problem, it is necessary to find the value of the angular acceleration of the body at the moment of time when the angular velocity ? equal to 6 rad/s.

First, you need to determine the derivative of the angular velocity with respect to time t in order to obtain the angular acceleration. Based on the formula for angular velocity, we can write:

? = 4 + 2t3 d?/dt = 6t2

Now, knowing the value of the derivative of the angular velocity, we can find the angular acceleration at the moment of time when ? = 6 rad/s:

d?/dt = 6t2 6 = 6t2 t2 = 1 t = 1

Thus, at the moment of time t=1 sec, the angular acceleration of the body will be equal to:

d2?/dt2 = 12 rad/s2

Answer: 12.

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