Question

The planet Mercury has a radius of 1500 miles and rotates one revolution every 1400 hours. What is the linear speed of a point on its equator in miles per hour?

Answer 1

`V = w C = 0.004488 (rad)/(hr) *3000 \pi mi = 42.298 (mi)/(hr)`

Explanation:

If we are in the equator we can assume a circular pattern and we can find the angular velocity like this:

`w = (1 rev)/(1400 hr) *(2\pi rad)/(1 rev)= 0.004488 rad/hr`

After we have this we can find the total distance travelled finding the circumference length of the planet Mercury at the equator with the following formula:

`C = 2 \pi R`

And we can replace the values given and we got:

`C = 2\pi *1500 mi =3000 \pi mi`

Now we can find the linear speed using this formula between the circumference and the angular velocity:

`V = w C = 0.004488 (rad)/(hr) *3000 \pi mi = 42.298 (mi)/(hr)`

And that would be the linear velocity required for this case.