Solution of problem 9.3.5 from the collection of Kepe O.E.

9.3.5 Does drum 1 rotate in accordance with the law? = 0.3t2. It is necessary to determine the angular acceleration of block 2 if the radii are R = 0.1 m and r = 0.06 m. The answer is 0.5.

To solve this problem, you need to use the formula for angular acceleration:

α = a / R,

where α is the angular acceleration, a is the linear acceleration, R is the radius of the circle along which the point moves.

We know that the speed of a point on the reel is determined by the formula:

v = Rω,

where v is the speed of a point on the drum, ω is the angular speed.

Linear acceleration is defined as the derivative of speed with respect to time:

a = dv / dt = R dω / dt,

where dω/dt is the angular acceleration.

Thus, angular acceleration can be expressed as:

dω / dt = a / R.

To find the angular acceleration, it is necessary to express the linear acceleration a through the equation of motion of a point on the drum:

s = Rθ,

where s is the length of the arc traversed by a point on the drum, θ is the angle through which the drum is rotated.

From the equation of motion we can express speed and linear acceleration:

v = ds / dt = R dθ / dt,

a = dv / dt = R d2θ / dt2.

Thus, angular acceleration can be expressed as:

α = a / R = d2θ / dt2.

From the law of drum motion it is known that the angle of rotation of the drum θ depends on time t as follows:

θ = (1/2) * 0.3 * t^2.

Let's differentiate this expression twice to find the angular acceleration:

dθ / dt = 0.3 * t,

d2θ / dt2 = 0.3.

Thus, the angular acceleration of block 2 is 0.3 m/s^2 / 0.06 m = 0.5 rad/s^2.

Solution to problem 9.3.5 from the collection of Kepe O.?.

This digital product is a solution to problem 9.3.5 from the collection of problems in physics by Kepe O.?. The problem is the calculation of the angular acceleration of block 2 when drum 1 rotates according to a given law of the dependence of the angle of rotation on time.

The solution to this problem is presented in the form of a detailed algorithm that will help you solve this problem easily and quickly. In addition, the solution uses basic formulas and principles of physics, which allows you to deepen your knowledge in this area.

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By purchasing this digital product, you receive a high-quality solution to the problem, which will help you better understand the material in physics and successfully cope with similar problems in the future.

This digital product is a solution to problem 9.3.5 from the collection of problems in physics by Kepe O.?. The task is to determine the angular acceleration of block 2 when drum 1 rotates according to a given law of the dependence of the angle of rotation on time. The solution to this problem is presented in the form of a detailed algorithm using basic formulas and principles of physics.

To solve the problem, it is necessary to use the formula for angular acceleration: α = a / R, where α is angular acceleration, a is linear acceleration, R is the radius of the circle along which the point moves. From the equation of motion of a point on a drum, we can express the speed and linear acceleration. Thus, angular acceleration can be expressed in terms of the rotation angle of the drum and its time derivatives.

To solve the problem, the law of drum motion is used, which is described by the equation? = 0.3t2, where ? - drum rotation angle, t - time. By differentiating this expression twice, we can find the angular acceleration of block 2.

So, the angular acceleration of block 2 for these radius values ​​is 0.5 rad/s^2. By purchasing this digital product, you receive a high-quality solution to the problem, which will help you better understand the material in physics and successfully cope with similar problems in the future.

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The book "Collection of problems for the course of higher mathematics" by Kepe O.?. contains solutions to problems, including problem 9.3.5. This problem can be described as follows: it is required to find a particular solution to the differential equation specified in the condition using the method of variation of constants. The solution requires the use of mathematical operations, such as integration and finding derivatives, as well as the use of appropriate formulas and properties of functions. The solution to the problem is presented in the book in detail with explanations and intermediate calculations.

Solution to problem 9.3.5 from the collection of Kepe O.?. requires determining the angular acceleration of block 2 based on the given law of rotation of drum 1.

According to the conditions of the problem, the radii of block 2 and drum 1 are equal to R = 0.1 m and r = 0.06 m, respectively, and the law of rotation of drum 1 is given by the equation ? = 0.3t2, where ? is the rotation angle of the drum in radians, and t is the time in seconds.

To solve the problem, it is necessary to determine the angular acceleration of block 2, which can be expressed through the linear acceleration of the block and the radius of the block. In turn, the linear acceleration of block 2 depends on the linear speed of the block, which can be expressed through the speed of a point on the surface of the drum in contact with the block. Thus, to solve the problem, it is necessary to determine the speed of a point on the surface of the drum in contact with the block and, based on it, calculate the linear speed and acceleration of block 2.

Since the law of rotation of the drum is given, it is possible to calculate the angular velocity of the drum at any time using the derivative of this law. For a given equation of the rotation law we obtain:

? = 0.3t^2 ?` = 0.6t

where ?` is the angular velocity of the drum in rad/s.

The speed of a point on the surface of the drum in contact with the block is equal to the product of the angular speed of the drum and its radius:

v = R * ?`

where v is the linear speed of a point on the surface of the drum in m/s.

The linear speed of block 2 in contact with this point is equal to the linear speed of the point on the surface of the drum:

v2 = v

The linear acceleration of block 2 can be expressed in terms of the angular acceleration of the drum and the radius of the block:

a2 = R * ?

where a2 is the linear acceleration of block 2 in m/s^2.

Thus, the angular acceleration of block 2 will be equal to:

?2 = a2 / R = ?

where ?2 is the angular acceleration of block 2 in rad/s^2.

Substituting expressions for the angular velocity of the drum and the linear velocity of a point on its surface, we obtain:

?2 = a2 / R = v / R^2 = (? * R) / R^2 = ? / R

Using the value of the angular velocity of the drum ?` = 0.6t and the given values ​​of the radii R and r, we obtain:

?2 = ?` / R = (0,6t) / 0,1 = 6t

Finally, to determine the angular acceleration of block 2, it is necessary to substitute the value of time t, which is not specified in the problem statement, into the resulting expression. Therefore, the answer to the problem can only be obtained with a known time value t. If the time value is unknown, then the answer to the problem cannot be determined.

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