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Answer :
The value of the angular acceleration of the second hand of the clock on the wall is D) 0 rad/s².
The angular acceleration of the second hand of the clock on the wall can be calculated using the formula:
Angular Acceleration (α) = (Change in Angular Velocity) / (Time Taken)
1. The second hand completes one full revolution in 60 seconds, which is the time taken for it to move from the 12 o'clock position to the 12 o'clock position again.
2. The change in angular velocity is the difference in angular velocity at the final and initial points. Since the second hand starts and ends at the same position, the change in angular velocity is 0
3. Plugging in the values:
α = 0 / 60 = 0 rad/s²
Thus, the angular acceleration of the second hand is 0 rad/s², making the correct answer option D) 0 rad/s².
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The value of angular acceleration of the second hand of a clock on the wall is zero (D) O rad/s².
The angular acceleration of the second hand of a clock on the wall is zero (D) O rad/s² because the second hand moves consistently at a constant angular velocity, completing one full revolution every 60 seconds. Since the angular velocity remains constant, the angular acceleration is zero.
Angular acceleration (α) is a measure of how the angular velocity (ω) of an object changes with respect to time (t). Mathematically, it is defined as:
α = Δω / Δt
Where:
α is the angular acceleration.
Δω is the change in angular velocity.
Δt is the change in time.
In the context of the second hand of a clock on the wall, we can consider its motion. The second hand moves in a circle with a constant angular speed because it takes exactly 60 seconds to complete one full revolution (360 degrees). Since the angular speed is constant, there is no change in angular velocity over time.
In other words, from the moment the second hand starts moving until it completes a full rotation and restarts, its angular velocity remains the same. This means Δω (change in angular velocity) is zero, and since angular acceleration is the rate of change of angular velocity, α is also zero.
Therefore, the angular acceleration of the second hand of the clock on the wall is indeed 0 rad/s². It maintains a constant angular speed as it moves in a circular path, and there is no acceleration or change in that speed.
Question: Why does the second hand of a wall clock experience little to no angular acceleration during its motion?
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