Question

Точка рухається рівномірно по колу радіусу R= 1.5м з кутовою швидкістю 3 рад/ с. Визначте лінійну швидкість точки, період та частоту її руху.

Answer 1

Відповідь: Див. додаток

Пояснення:

Answer 2

Calculation of Linear Velocity, Period, and Frequency

To determine the linear velocity, period, and frequency of a point moving uniformly along a circular path with a radius of 1.5 meters and an angular velocity of 3 radians per second, we can use the following formulas:

1. Linear Velocity (v): - The linear velocity of a point moving along a circular path is given by the formula: v = r * ω, where v is the linear velocity, r is the radius of the circular path, and ω is the angular velocity. - Substituting the given values, we have: v = 1.5 m * 3 rad/s. - Evaluating the expression, we find that the linear velocity of the point is 4.5 m/s.

2. Period (T): - The period of a point moving along a circular path is the time taken for the point to complete one full revolution. - The period can be calculated using the formula: T = 2π / ω, where T is the period and ω is the angular velocity. - Substituting the given value, we have: T = 2π / 3 rad/s. - Evaluating the expression, we find that the period of the point is approximately 2.094 seconds.

3. Frequency (f): - The frequency of a point moving along a circular path is the number of complete revolutions made by the point in one second. - The frequency can be calculated using the formula: f = 1 / T, where f is the frequency and T is the period. - Substituting the calculated value of the period, we have: f = 1 / 2.094 s. - Evaluating the expression, we find that the frequency of the point is approximately 0.478 Hz.

Therefore, the linear velocity of the point is 4.5 m/s, the period of its motion is approximately 2.094 seconds, and the frequency of its motion is approximately 0.478 Hz.