circular motion dynamics

Question

A stone of mass 0.5 kg tied to a string of length 1 m is whirled in a horizontal circle at 2 revolutions per second. What is the centripetal force?

RankGuru · Accepted Answer

1. **Angular Velocity ($\omega$)**: $2$ revolutions/sec means frequency $f = 2$ Hz.
   - $\omega = 2\pi f = 4\pi$ rad/s.
2. **Centripetal Force Formula**: $F = m \omega^2 r$.
3. **Application**:
   - $F = 0.5 	ext{ kg} 	imes (4\pi)^2 	imes 1 	ext{ m}$.
   - $F = 0.5 	imes 16 \pi^2 = 8\pi^2$.
4. **Numerical Evaluation**: Taking $\pi^2 \approx 9.87$:
   - $F = 8 	imes 9.87 = 78.96$ N.
5. **Note**: This force is provided by the tension in the string.

Rank Guru

circular motion dynamics

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