QuestionMay 28, 2025

A coin completes 18 spins in 12 seconds The centripetal acceleration of the edge of the coin is 2.2m/s^2 The radius of the coin is square m

A coin completes 18 spins in 12 seconds The centripetal acceleration of the edge of the coin is 2.2m/s^2 The radius of the coin is square m
A coin completes 18 spins in 12 seconds The centripetal acceleration of the edge of the coin is 2.2m/s^2
The radius of the coin is square  m

Solution
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Answer

The radius of the coin is approximately 0.0778 m. Explanation 1. Calculate angular velocity Angular velocity \omega = \frac{2\pi \times \text{spins}}{\text{time}} = \frac{2\pi \times 18}{12} = 3\pi \, \text{rad/s}. 2. Use centripetal acceleration formula Centripetal acceleration a_c = \omega^2 \times r. Given a_c = 2.2 \, \text{m/s}^2, solve for r: r = \frac{a_c}{\omega^2} = \frac{2.2}{(3\pi)^2}.

Explanation

1. Calculate angular velocity<br /> Angular velocity $\omega = \frac{2\pi \times \text{spins}}{\text{time}} = \frac{2\pi \times 18}{12} = 3\pi \, \text{rad/s}$.<br />2. Use centripetal acceleration formula<br /> Centripetal acceleration $a_c = \omega^2 \times r$. Given $a_c = 2.2 \, \text{m/s}^2$, solve for $r$: $r = \frac{a_c}{\omega^2} = \frac{2.2}{(3\pi)^2}$.
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