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4 part Physics Help Please?
The earth's radius is 6.37×106m; it rotates once every 24 hours.
A)What is the earth's angular speed?
B)Viewed from a point above the north pole, is the angular velocity positive or negative?
C) What is the speed of a point on the equator?
D) What is the speed of a point on the earth's surface located at 3/5 of the length of the arc between the equator and the pole, measured from equator? (Hint: what is the radius of the circle in which the point moves?)
PLEASE EXPLAIN ALL PARTS OF EQUATION AND WHAT THEY MEAN FOR BEST ANSWER.(please don't just put pi rad MR etc explain what it is)
1 Answer
- 5 years ago
A) Use the equation ω=∆θ/∆t to find the angular speed. θ=2π and t=24 hrs/3600s (because you have to convert to seconds for rad/s). If you plug the numbers in you get 2π/(24÷3600s)=7.3x10^(-5) rad/s
B) ω is positive for counter-clockwise rotation and negative in the clockwise direction. From the north pole, you see that the Earth rotates counter-clockwise, so ω is positive.
C) For this, we are looking at the tangential velocity. The equation for this is v_t=rω. As given, we know that r=6.37×10^6 m. We also know ω from A. Plug those in to get v_t=(6.37×10^6 m)(7.3x10^(-5) rad/s) = 463 m/s
D) The angular difference between the equator and the north pole is 90º. 3/5 of that would be 54º. Using rules for trig, you can find that the radius at that point is r=(Earth's radius)cos54º=3.74x10^6. Then you plug that into the v_t=rω equation again to get v_t=(3.74x10^6)(7.3x10^(-5) rad/s)=272 m/s
*I had a different angle for this, so check with you calculator to make sure I didn't make any errors.
Hope that helps.
