Question

Сравните ускорения секундной и минутной стрелок одинаковой длины.

Answer 1

Формула нормального (центробежного ускорения):
a = (4π²/R)/T²

Секундная стрелка = (4π²/R) / 60² = (4π²/R)/3600
Минутная стрелка = (4π²/R) / ((60²)²) = (4π²/R)/3600²

Сравниваем их: ((4π²/R)/3600) / ((4π²/R)/3600²) = 3600.

Ответ: Ускорение секундной стрелки в 3600 раз больше ускорения минутной стрелки.

Answer 2

Comparison of Accelerations of Second and Minute Hands of Equal Length

When comparing the accelerations of the second and minute hands of a clock, it is important to consider their respective lengths and rotational speeds.

The second hand completes one full revolution in 60 seconds, while the minute hand completes one full revolution in 60 minutes. Since both hands have the same length, their angular velocities are different. The angular velocity of the second hand is much higher than that of the minute hand.

To calculate the acceleration of each hand, we need to consider the centripetal acceleration, which is given by the formula:

a = ω²r

Where: - a is the centripetal acceleration - ω is the angular velocity - r is the radius or length of the hand

Since the length of both hands is the same, we can assume that the radius is constant. Therefore, the acceleration of each hand depends solely on its angular velocity.

Given that the angular velocity of the second hand is higher than that of the minute hand, we can conclude that the acceleration of the second hand is also higher.

Please note that the exact values of the accelerations would require specific measurements of the lengths and angular velocities of the hands. However, based on the general understanding of clock mechanics, we can confidently state that the second hand has a higher acceleration compared to the minute hand.