Question

Через неподвижный блок с моментом инерции 0,1 кг м2 и радиусом 0,15 м перекинута нить с грузами 1,5 кг и 3 кг. Найдите угловое ускорение грузов во время движения.

Answer 1

Пусть m1 = 1,5 кг
          m2 = 3 кг
           J блока = 0,1 кг ·м²
           R = 0,15 м

Найдем массу блока:
m = 2*J/R² ≈ 8,9 кг

Составляя уравнения движения грузов, получаем ускорения грузов:
a = (m2 - m1) * g /(m2 + m1 +m/2) = (3 - 1,5)*10/(3+1,5+8,9/2) ≈ 1,7 м/с²

Ответ а = 1,7 м/с²

(Только мне кажется, что это НЕ ШКОЛЬНАЯ задача, а задача по ОБЩЕЙ ФИЗИКЕ вуза ????? )

Answer 2

Calculation of Angular Acceleration

To find the angular acceleration of the masses during their motion, we can use the principle of conservation of angular momentum. The formula for angular momentum is given by:

L = Iω

Where: - L is the angular momentum - I is the moment of inertia - ω is the angular velocity

In this case, the moment of inertia of the system is given as 0.1 kg·m^2, and the radius is 0.15 m. The masses of the objects are 1.5 kg and 3 kg.

To calculate the angular acceleration, we need to find the initial and final angular velocities of the system.

Since the system starts from rest, the initial angular velocity is 0.

To find the final angular velocity, we can use the principle of conservation of angular momentum. The total angular momentum of the system before and after the motion should be the same.

Let's denote the initial moment of inertia as I_initial and the final moment of inertia as I_final.

The initial angular momentum is given by:

L_initial = I_initial * ω_initial = 0.1 kg·m^2 * 0 = 0

The final angular momentum is given by:

L_final = I_final * ω_final

Since the moment of inertia remains constant, we can rewrite the equation as:

L_final = I_initial * ω_final

Since the total angular momentum is conserved, we have:

L_initial = L_final

Substituting the values, we get:

0 = 0.1 kg·m^2 * ω_final

Solving for ω_final, we find that ω_final is also 0.

Since the final angular velocity is 0, the angular acceleration is also 0.

Therefore, the angular acceleration of the masses during their motion is 0 rad/s^2.