Question

Линейная скорость точки на поверхности колеса равна 0.4 м/с. диаметр окружности по которой движется точка равен 16 см. Какова частота вращения колеса? Сколько оборотов совершает колесо за 1 минуту?

Answer 1

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Answer 2

Calculation of Wheel's Angular Velocity

To find the angular velocity of the wheel, we can use the formula:

Angular velocity (ω) = Linear velocity (v) / Radius (r)

Given that the linear velocity of the point on the wheel's surface is 0.4 m/s and the diameter of the circle along which the point moves is 16 cm, we can calculate the radius as half of the diameter:

Radius (r) = Diameter (d) / 2

Substituting the values, we have:

Radius (r) = 16 cm / 2 = 8 cm = 0.08 m

Now, we can calculate the angular velocity:

Angular velocity (ω) = 0.4 m/s / 0.08 m = 5 rad/s

Calculation of Wheel's Rotation Frequency

To find the rotation frequency of the wheel, we can use the formula:

Rotation frequency (f) = Angular velocity (ω) / (2π)

Substituting the value of the angular velocity we calculated earlier, we have:

Rotation frequency (f) = 5 rad/s / (2π) ≈ 0.796 Hz

Calculation of Wheel's Number of Revolutions in 1 Minute

To find the number of revolutions the wheel makes in 1 minute, we can use the formula:

Number of revolutions = Rotation frequency (f) * Time (t)

Given that the time is 1 minute, we can substitute the values:

Number of revolutions = 0.796 Hz * 1 min ≈ 0.796 revolutions

Therefore, the wheel makes approximately 0.796 revolutions in 1 minute.

Please note that the calculations are based on the given information and assumptions.