The earth’s rotation axis, which is tilted 23 . 5 ° from the plane of the earth’s orbit, today points to Polaris, the north star. But Polaris has not always been the north star because the earth, like a spinning gyroscope, precesses. That is, a line extending along the earth’s rotation axis traces out a 23.50 cone as the earth precesses with a period of 26,000 years. This occurs because the earth is not a perfect sphere. It has an equatorial bulge , which allows both the moon and the sun to exert a gravitational torque on the earth. Our expression for the precession frequency of a gyroscope can be written Ω = τ / I ω . Although we derived this equation for a specific situation, it’s a valid result, differing by at most a constant close to 1, for the precession of any rotating object. What is the average gravitational torque on the earth due to the moon and the sun?
The earth’s rotation axis, which is tilted 23 . 5 ° from the plane of the earth’s orbit, today points to Polaris, the north star. But Polaris has not always been the north star because the earth, like a spinning gyroscope, precesses. That is, a line extending along the earth’s rotation axis traces out a 23.50 cone as the earth precesses with a period of 26,000 years. This occurs because the earth is not a perfect sphere. It has an equatorial bulge , which allows both the moon and the sun to exert a gravitational torque on the earth. Our expression for the precession frequency of a gyroscope can be written Ω = τ / I ω . Although we derived this equation for a specific situation, it’s a valid result, differing by at most a constant close to 1, for the precession of any rotating object. What is the average gravitational torque on the earth due to the moon and the sun?
The earth’s rotation axis, which is tilted
23
.
5
°
from the plane of the earth’s orbit, today points to Polaris, the north star. But Polaris has not always been the north star because the earth, like a spinning gyroscope, precesses. That is, a line extending along the earth’s rotation axis traces out a 23.50 cone as the earth precesses with a period of 26,000 years. This occurs because the earth is not a perfect sphere. It has an equatorial bulge, which allows both the moon and the sun to exert a gravitational torque on the earth. Our expression for the precession frequency of a gyroscope can be written
Ω
=
τ
/
I
ω
. Although we derived this equation for a specific situation, it’s a valid result, differing by at most a constant close to 1, for the precession of any rotating object. What is the average gravitational torque on the earth due to the moon and the sun?
The earth's radius is 6.37×106m6.37×106m; it rotates once every 24 hours.
What is the speed of a point on the earth's surface located at 2/52/5 of the length of the arc between the equator and the pole, measured from equator?
You have walked around the rim of a large circle whose radius is 2.1 miles. The GPS tells you that you have walked a path length of 8 miles. What angular distance (in radians) have you walked?
It takes 365.23 days for the earth to complete one revolution around the sun. Calculate the (a) period, (b) frequency, and (c) angular frequency of Earth as it revolves around the Sun.
Chapter 12 Solutions
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
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