A particle moves in a circular path with a radius of 4 m and completes one revolution in 8 seconds. What is the centripetal acceleration?

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Q: A particle moves in a circular path with a radius of 4 m and completes one revolution in 8 seconds. What is the centripetal acceleration?

Solution: Centripetal acceleration (a_c) = v²/r. First find v = 2πr/T = 2π(4)/8 = π m/s. Then a_c = (π)²/4 = 2.5 m/s².

Steps: 8

Step 1: Identify the radius of the circular path, which is given as 4 meters.
Step 2: Identify the time taken to complete one revolution, which is given as 8 seconds.
Step 3: Use the formula for linear velocity (v) in circular motion: v = (2πr) / T.
Step 4: Substitute the values into the formula: v = (2π * 4) / 8.
Step 5: Simplify the equation: v = (8π) / 8 = π m/s.
Step 6: Now, use the formula for centripetal acceleration (a_c): a_c = v² / r.
Step 7: Substitute the value of v and r into the formula: a_c = (π)² / 4.
Step 8: Calculate (π)², which is approximately 9.87, and then divide by 4: a_c ≈ 2.5 m/s².