mercury rotates around the sun in approx. 89 earth days (or 7,689,600 s. use a calculator to approximate its angular speed.
choices:
4.09x10^-7
0.035
0.071
8.17x10^-7
The angular speed is
(2π / 7.6896*10^6) rad/s
Well, if you really want me to use a calculator, I guess that means I have to stop clowning around for a moment. Fine, I'll do some actual math!
The formula for angular speed is angular speed = (2π)/time. So, to approximate the angular speed, we can use the formula angular speed ≈ (2π)/(89 Earth days in seconds).
Now, let's break out the trusty calculator...
(2π)/(89 * 24 * 60 * 60) ≈ 8.17 x 10^(-7)
So, it looks like the answer is 8.17 x 10^(-7). That's the approximate angular speed of Mercury around the sun. It may not be as funny as a clown, but hey, math can be amusing too!
To calculate the approximate angular speed of Mercury, we can use the formula:
Angular speed = 2π / Time taken
Given that the time taken is approximately 7,689,600 seconds, we can substitute it into the formula:
Angular speed ≈ 2π / 7,689,600
Using a calculator, we can now approximate the angular speed of Mercury:
Angular speed ≈ 2π / 7,689,600
≈ (2 * 3.14159) / 7,689,600
≈ 0.000816792627 rad/s
Rounding to the nearest decimal point, the approximate angular speed of Mercury is 8.17x10^-4 rad/s.
None of the given choices match the calculated value exactly, but the closest option is 8.17x10^-7.
To approximate the angular speed of Mercury, we need to calculate the number of radians Mercury moves through in one second.
The formula for angular speed is given by:
Angular speed (ω) = Δθ / Δt
Where:
Δθ is the change in angle (in radians)
Δt is the change in time (in seconds)
In this case, we know that Mercury rotates around the Sun in approximately 7,689,600 seconds (89 Earth days).
To find the angular speed, we need to calculate the change in angle and divide it by the change in time.
The change in angle for one complete revolution is 2π radians.
So, ω = (2π) / (7,689,600 seconds)
Using a calculator, we can evaluate this expression:
ω ≈ 8.17 x 10^-7 (rounded to 3 significant figures)
Therefore, the correct choice is 8.17x10^-7.