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Rotational Mechanics — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsRotational Mechanics2 Marks
Question
Because of the friction between the water in oceans with the earth's surface, the rotational kinetic energy of the earth is continuously decreasing. If the earth's angular speed decreases by 0.0016rad/ day in 100 years, find the average torque of the friction on the earth. Radius of the earth is 6400km and its mass is $6.0 \times 10^{24}kg$.
✓

Answer

The earth’s angular speed decreases by 0.0016rad/ day in 100 years. Therefore the torque produced by the ocean water in decreasing earth's angular velocity$\tau=\text{I}\alpha$
$=\frac{2}{5}\text{mr}^2\times\frac{(\omega-\omega_0)}{\text{t}}$
$=\frac{2}{6}\times6\times10^{24}\times64^2\times10^{10}\times\Big(\frac{0.0016}{26400^2\times100\times365}\Big)$ (1 year = 365 days= 365 × 56400 sec)
$=5.678\times10^{20}\text{N-m}$

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