Solution to problem 19.2.6 from the collection of Kepe O.E.

To determine the angular acceleration of gear 1, it is necessary to calculate the moment of forces acting on it. From the problem conditions it is known that a pair of forces with a moment M = 1.4 N • m is applied to the gear.

The moment of force can be calculated using the formula:

M = F * r * sin(a),

where F is the force applied to the gear; r - gear radius; α is the angle between the direction of the force and the radius of the gear.

Angle α in this problem is 90 degrees because the force is applied to the radius of the gear. Thus,

M = F * r.

Then the angular acceleration of the gear can be calculated using the formula:

α = M / (I1 + m2 * r^2),

where I1 is the moment of inertia of the gear relative to the axis of rotation, and m2 is the mass of the rack.

Substituting known values, we get:

α = 1.4 / (0.01 + 1 * 0.1^2) = 21 (rad/s^2).

Thus, the angular acceleration of the gear is 21 (rad/s^2).

Solution to problem 19.2.6 from the collection of Kepe O.?.

This digital product is a solution to problem 19.2.6 from the collection of problems in physics by Kepe O.?.

The problem requires determining the angular acceleration of a gear if a pair of forces is applied to it with a moment M = 1.4 N • m, rack mass m2 = 1 kg, moment of inertia of the gear relative to the axis of rotation I1 = 0.01 kg • m2, gear radius r = 0.1 m.

To solve the problem, it is necessary to apply formulas to calculate the torque and angular acceleration of the gear. The solution to this problem is described and illustrated in detail in the file.

By purchasing this digital product, you receive a complete and understandable solution to the problem, which will help you master the material and increase your level of knowledge in physics.

This digital product is a solution to problem 19.2.6 from the collection of problems in physics by Kepe O.?. The problem requires determining the angular acceleration of a gear if a pair of forces is applied to it with a moment M = 1.4 N • m, rack mass m2 = 1 kg, moment of inertia of the gear relative to the axis of rotation I1 = 0.01 kg • m2, gear radius r = 0.1 m.

To solve the problem, it is necessary to calculate the moment of forces acting on the gear using the formula M = F * r, where F is the force applied to the gear, and r is the radius of the gear. Then, the angular acceleration of the gear can be calculated using the formula α = M / (I1 + m2 * r^2), where I1 is the moment of inertia of the gear about the axis of rotation, and m2 is the mass of the rack.

The resulting angular acceleration of the gear is 21 (rad/s^2). The solution to this problem is described and illustrated in detail in the file that you will receive when purchasing this digital product. This solution will help you master the material and increase your level of knowledge in physics.

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Solution to problem 19.2.6 from the collection of Kepe O.?. consists in determining the angular acceleration of the gear if a pair of forces is applied to it with a moment M = 1.4 N•m, rack mass m2 = 1 kg, moment of inertia of the gear relative to the axis of rotation I1 = 0.01 kg•m2, gear radius r = 0.1 m.

To solve the problem, you need to use the equation of dynamics of rotational motion:

М = Iα,

where M is the moment of force, I is the moment of inertia, α is angular acceleration.

The moment of inertia of the gear relative to the axis of rotation is equal to I1, so we can write:

M = I1α.

Substituting the values, we get:

1.4 Н•м = 0.01 kg•м2 * a.

From here we find the angular acceleration:

α = 1.4 N•m / 0.01 kg•m2 = 140 rad/s2.

So, the answer to problem 19.2.6 from the collection of Kepe O.?. equal to 140 rad/s2.

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