9.67 A vinyl record that is initially turning at 33 frac{1}{3} mathrm{rpm} slows uniformly to a stop in a time of 15.0 mathrm{~s}. How many rotations are made by the record while stopping?

Question

Accepted Answer

Step:1 ：Convert initial angular velocity from rpm to rad/s: (omega_{i} = 33.33 times frac{2pi}{60} = 3.49 , rad/s)Step:2 ：Calculate angular displacement: (theta = frac{omega_{i} + omega_{f}}{2} times t = frac{3.49 + 0}{2} times 15 = 26.18 , rad)Step:3 ：Find the number of rotations: (n = frac{theta}{2pi} = frac{26.18}{2pi} approx 4.17)Step:4 ：(boxed{4.17}) rotations

Answer

Step: 1 ：Convert initial angular velocity from rpm to rad/s: (omega_{i} = 33.33 times frac{2pi}{60} = 3.49 , rad/s)Step: 2 ：Calculate angular displacement: (theta = frac{omega_{i} + omega_{f}}{2} times t = frac{3.49 + 0}{2} times 15 = 26.18 , rad)Step: 3 ：Find the number of rotations: (n = frac{theta}{2pi} = frac{26.18}{2pi} approx 4.17)Step: 4 ：(boxed{4.17}) rotations

9.67 A vinyl record that is initially turning at $33 \frac{1}{3} \mathrm{rpm}$ slows uniformly to a stop in a time of $15.0 \mathrm{~s}$. How many rotations are made by the record while stopping?

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