1. Understanding Circular Motion
The tip of the second hand undergoes uniform circular motion. This means it moves in a circle at a constant speed. However, its velocity (which includes direction) is constantly changing because the direction of motion is always tangent to the circle. This change in velocity is what causes acceleration.
2. Centripetal Acceleration
The acceleration experienced by an object in uniform circular motion is called centripetal acceleration. It always points towards the center of the circle and is given by:
* a = v²/r
Where:
* a = centripetal acceleration
* v = speed of the object (tangential velocity)
* r = radius of the circular path
3. Calculating the Speed
* The second hand completes a full circle (2π radians) in 60 seconds.
* Angular speed (ω) = 2π radians / 60 seconds = π/30 radians/second
* Linear speed (v) = ωr = (π/30 radians/second) * (1.7 cm) = 0.17π cm/second
4. Calculating the Acceleration
* a = v²/r = (0.17π cm/second)² / (1.7 cm) ≈ 0.053π² cm/second²
Result
The magnitude of the acceleration experienced by the tip of the second hand is approximately 0.053π² cm/second² or about 0.52 cm/second².
Important Notes:
* This is a relatively small acceleration, much less than the acceleration due to gravity (9.8 m/s²).
* The actual acceleration might be slightly different depending on the exact length of the second hand on your watch.
