The Earth takes slightly less than one day to complete one rotation about the axis passing through its poles. The actual time is 8.616 × 10⁴ s. Given this information, what is the angular speed of the Earth about its axis? A)7.292 × 10^-⁵ rad/s B)2.321 × 10^-⁶ rad/s C)9.951 × 10^-⁵ rad/s D)6.334 × 10^-⁴ rad/s E)1.990 × 10^-⁷ rad/s

Question

Quizplus · Accepted Answer

We can use the formula for angular speed (ω) which is given by:

ω = Δθ/Δt

where Δθ is the angular displacement and Δt is the time interval.

In one day, the Earth completes one full rotation, which means the angular displacement is 2π radians. Therefore,

ω = Δθ/Δt = 2π/8.616 × 10^14 s

Simplifying this expression gives:

ω = 7.292 × 10^-5 rad/s

which is approximately equal to 7.292 × 10^1^–15 rad/s in scientific notation. Therefore, the correct answer is A.

The Earth Takes Slightly Less Than One Day to Complete