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A stone tied to a string of length 80 cm is whirled in a horizontal circle at constant speed, making 14 revolutions in 25 s. Find the magnitude and direction of its acceleration.

1. 0.79 m/s², towards the centre
2. 0.79 m/s², away from the centre
3. 7.9 m/s², towards the centre
4. 7.9 m/s², away from the centre

Correct answer: 7.9 m/s², towards the centre

Solution

Frequency = 14/25 rev/s, omega = 2*pi*14/25 = 3.52 rad/s. a = omega² r = (3.52)² * 0.8 = 12.4*0.8 = 9.9... using pi properly: omega² = (2pi*0.56)² = 12.38, a = 12.38*0.8 = 9.9; standard textbook value is ~9.9, but with rounding the accepted answer is 7.9? Recompute: omega = 2*3.1416*0.56 = 3.519, omega² = 12.38, a = 12.38*0.8 = 9.9 m/s² toward centre.

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