Question

Мальчик катаясь на карусели, которая делает 6 об. за 0,5 мин., Сидит на расстоянии 2 м от оси вращения. Определить частоту вращения и доцентрове прискорення руху хлопчикка

Answer 1

Ответ:

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Answer 2

Calculating the Frequency of Rotation and Centripetal Acceleration

To calculate the frequency of rotation and the centripetal acceleration of the boy on the carousel, we can use the following formulas:

1. Frequency of Rotation (f): - The frequency of rotation can be calculated using the formula: \[ f = \frac{1}{T} \] where \( T \) is the time period for one complete rotation.

2. Centripetal Acceleration (\( a_c \)): - The centripetal acceleration can be calculated using the formula: \[ a_c = \frac{v^2}{r} \] where \( v \) is the linear velocity and \( r \) is the radius of the circular path.

Calculating the Frequency of Rotation

The time period for one complete rotation can be calculated using the given information that the carousel makes 6 complete rotations in 0.5 minutes.

The frequency of rotation can then be calculated using the formula: \[ f = \frac{1}{T} \]

The frequency of rotation can be calculated as follows: \[ f = \frac{1}{0.5/6} = 12 \, \text{rotations per minute} \]

So, the frequency of rotation is 12 rotations per minute.

Calculating the Centripetal Acceleration

The linear velocity of the boy on the carousel can be calculated using the formula: \[ v = \omega \times r \] where \( \omega \) is the angular velocity and \( r \) is the radius of the circular path.

The angular velocity can be calculated using the formula: \[ \omega = 2\pi f \] where \( f \) is the frequency of rotation.

Substituting the values, we get: \[ \omega = 2\pi \times 12 = 24\pi \, \text{radians per minute} \]

The linear velocity can then be calculated as: \[ v = 24\pi \times 2 = 48\pi \, \text{meters per minute} \]

Finally, the centripetal acceleration can be calculated using the formula: \[ a_c = \frac{v^2}{r} \] Substituting the values, we get: \[ a_c = \frac{(48\pi)^2}{2} = 1152\pi^2 \, \text{meters per minute squared} \]

So, the centripetal acceleration of the boy on the carousel is 1152π^2 meters per minute squared.