The Centripetal Acceleration of the Earth (a) What is the centripetal acceleration of the Earth as it moves in its orbit around the Sun? SOLUTION Conceptualize Think about a mental image of the Earth in a circular orbit around the Sun. We will model the Earth as -Select-- and approximate the Earth's orbit as circular (it's actually slightly elliptical). Categorize The Conceptualize step allows us to categorize this problem as one of a particle -Select- Analyze We do not know the orbital speed of the Earth to substitute into this equation: (1) With the help of the following equation, 2ar (2) ....................... however, we can recast Equation (1) in terms of the period of the Earth's orbit, which we know is-Select Vi and the radius of the Earth's orbit around the Sun, which is 1.496 x 10 m. (Use the following as necessary: r and T.) Combine Equations (1) and (2): Substitute numerical values to find the centripetal acceleration (in m/s): m/s² (b) What is the angular speed of the Earth in its orbit around the Sun? SOLUTION Substitute numerical values into the equation a = to find the angular speed (in rad/s): rad/s
The Centripetal Acceleration of the Earth (a) What is the centripetal acceleration of the Earth as it moves in its orbit around the Sun? SOLUTION Conceptualize Think about a mental image of the Earth in a circular orbit around the Sun. We will model the Earth as -Select-- and approximate the Earth's orbit as circular (it's actually slightly elliptical). Categorize The Conceptualize step allows us to categorize this problem as one of a particle -Select- Analyze We do not know the orbital speed of the Earth to substitute into this equation: (1) With the help of the following equation, 2ar (2) ....................... however, we can recast Equation (1) in terms of the period of the Earth's orbit, which we know is-Select Vi and the radius of the Earth's orbit around the Sun, which is 1.496 x 10 m. (Use the following as necessary: r and T.) Combine Equations (1) and (2): Substitute numerical values to find the centripetal acceleration (in m/s): m/s² (b) What is the angular speed of the Earth in its orbit around the Sun? SOLUTION Substitute numerical values into the equation a = to find the angular speed (in rad/s): rad/s
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Question
Transcribed Image Text:The Centripetal Acceleration of the Earth
(a) What is the centripetal acceleration of the Earth as it moves in its orbit around the Sun?
SOLUTION
Conceptualize Think about a mental image of the Earth in a circular orbit around the Sun. We will model the Earth as [-Select--
Vand approximate the Earth's orbit as circular (it's actually slightly elliptical).
Categorize The Conceptualize step allows us to categorize this problem as one of a particle --Select-
Analyze We do not know the orbital speed of the Earth to substitute into this equation:
(1)
With the help of the following equation,
2ar
T-
(2)
.*..................
however, we can recast Equation (1) in terms of the period of the Earth's orbit, which we know isSelect- V: and the radius of the Earth's orbit around the Sun, which is 1.496 x 10** m.
............. .
(Use the following as necessary: r and T.)
Combine Equations (1) and (2):
a
Substitute numerical values to find the centripetal acceleration (in m/s):
m/s²
(b) What is the angular speed of the Earth in its orbit around the Sun?
SOLUTION
Substitute numerical values into the equation o =
to find the angular speed (in rad/s):
rad/s
Transcribed Image Text:Finaliee The acceleration in part (a) much smaler than the free fall acceleration on the surface of the Earth
r the metien. In many prems,Rmere kly that Fikown ther than v. In part (b, we see that the anguler s
very amal, which ate be epected becne the tarth takes an entire
EXERCISE
A wheel 0.60 min reus rotates contant te f 100 rewmin. Find the speed
Hiat
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