Answer to Question #174451 in Classical Mechanics for Rohan

Question #174451

In one second the earth rotates about its axis by an angle θ where


(a) θ < 10-6  radian


(b) 10-6 radian< θ< 10-5 radian


(c) 10-5 radian < θ < 10-4 radian


(d) θ > 10-4 radian


1
Expert's answer
2021-03-29T09:04:20-0400

Let's first find the angular speed of Earth's rotation about its axis:


ω=ΔθΔt,\omega=\dfrac{\Delta \theta}{\Delta t},ω=2π rad1 d1 d24 h3600 s1 h=7.27105 rads.\omega=\dfrac{2\pi\ rad}{1\ d}\cdot\dfrac{1\ d}{24\ h\cdot3600\ \dfrac{s}{1\ h}}=7.27\cdot10^{-5}\ \dfrac{rad}{s}.

Then, in one second the Earth rotates about its axis by an angle θ\theta equals:


θ=ωt,\theta=\omega t,θ=7.27105 rads1 s=7.27105 rad.\theta=7.27\cdot10^{-5}\ \dfrac{rad}{s}\cdot1\ s=7.27\cdot10^{-5}\ rad.

Therefore, the correct answer is (c).

Answer:

(c) 10-5 radian < θ < 10-4 radian.


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