Solution to problem 16.1.11 from the collection of Kepe O.E.

16.1.11 Determine the angular acceleration of a disk of radius r = 0.3 m and mass m = 50 kg, if the tensions of the driving and driven branches of the belt are respectively equal to T1 = 2Т2 = 100N. The radius of inertia of the disk relative to the axis of rotation is 0.2 m. (Answer 7.5)

To solve the problem, it is necessary to use the formula for the moment of inertia of a rigid body: $I = \frac{mR^2}{2}$, where m is the mass of the body, R is its radius.

You will also need Newton's second law for rotational motion: $M = I\alpha$, where M is the moment of forces acting on the body, $\alpha$ is the angular acceleration.

The tension of the driving belt branch is equal to the friction force acting on the disk, and the tension of the driven belt branch is equal to the moment of the friction force acting on the disk: $T_1 = F_{tr}$, $T_2 = \frac{M_{tr}}{R}$ , where $F_{tr}$ is the friction force, $M_{tr}$ is the moment of the friction force.

Since the disk is in equilibrium, $T_1 = 2T_2$. From here we find $T_2 = \frac{T_1}{2} = 50$ N.

Substituting the known values ​​into the formula for the moment of inertia, we obtain: $I = \frac{50 \cdot 0.3^2}{2} = 2.25$ kg$\cdot$m$^2$.

Using Newton's second law for rotational motion, we find the angular acceleration: $\alpha = \frac{M}{I} = \frac{T_2 \cdot R}{I} = \frac{50 \cdot 0.3}{2, 25} \approx 6.67$ rad/s$^2$.

Answer: 6.67 rad/s$^2$ (rounded to one decimal place).

Solution to problem 16.1.11 from the collection of Kepe O.?.

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The product is the solution to problem 16.1.11 from the collection of Kepe O.?. The problem is to determine the angular acceleration of a disk of radius r = 0.3 m and mass m = 50 kg. The tensions of the driving and driven branches of the belt are respectively equal to T1 = 2Т2 = 100 N. The radius of inertia of the disk relative to the axis of rotation is 0.2 m.

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

α = (T1 - T2) * r / (I * m),

where T1 and T2 are the tensions of the driving and driven branches of the belt, r is the radius of the disk, I is the radius of inertia of the disk relative to the axis of rotation, m is the mass of the disk.

Substituting the known values, we get:

α = (100 N - 50 N) * 0.3 m / (0.2 m * 50 kg) = 7.5 rad/s².

Answer: the angular acceleration of the disk is 7.5 rad/s².

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