Question

Помогите пожалуйста решить задачу! Материальная точка движется по окружности по закону φ = A + B*t5, где A = 1 рад, B = 2 рад/с5. Определите угловое ускорение точки в момент времени 2 с. Является ли такое движение равноускоренным или нет и почему?

Answer 1

Ответ. u(t)= A + B*t^5; w(t)=du(t)/dt=5*B*t^4; e(t)=dw(t)/dt=20*B*t^3; e(2)=20*2*2^3=320;

Answer 2

Problem Analysis

We are given that a material point is moving along a circular path with a law of motion described by the equation φ = A + B*t^5, where A = 1 rad and B = 2 rad/s^5. We need to determine the angular acceleration of the point at t = 2 s and determine whether this motion is uniformly accelerated or not.

Angular Acceleration Calculation

To find the angular acceleration, we need to differentiate the equation for angular displacement (φ) with respect to time (t). Taking the derivative of φ = A + B*t^5 with respect to t, we get:

dφ/dt = d(A + B*t^5)/dt = 0 + 5*B*t^4 = 5*B*t^4

Now, we can substitute the given values of B = 2 rad/s^5 and t = 2 s into the equation to find the angular acceleration at t = 2 s:

dφ/dt = 5*B*t^4 = 5*(2 rad/s^5)*(2 s)^4 = 5*2*(16 s^4) = 160 rad/s^4

Therefore, the angular acceleration of the point at t = 2 s is 160 rad/s^4.

Uniformly Accelerated Motion

To determine whether this motion is uniformly accelerated or not, we need to check if the angular acceleration is constant. In this case, the angular acceleration is not constant because it depends on the time (t) through the term t^4 in the equation. Therefore, the motion described by the equation φ = A + B*t^5 is not uniformly accelerated.

Summary

- The angular acceleration of the point at t = 2 s is 160 rad/s^4. - The motion described by the equation φ = A + B*t^5 is not uniformly accelerated because the angular acceleration is not constant.

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