Rotation of sphere problem, acceleration and velocity

In summary, the conversation discusses the time it takes for the Earth to make one revolution (23 hours 56 minutes and 4 seconds) and the resulting angular speed (7.29×10-5 rad/s). It also mentions the linear speed of an object on the surface of the Earth and the acceleration of this object, and provides equations for calculating these values. However, there is a discrepancy in the given value for the Earth's rotation period, which affects the accuracy of the calculations.
  • #1
Staerke
12
0

Homework Statement



It takes 23 hours 56 minutes and 4 seconds for the Earth to make one revolution (mean sidereal day). What is the angular speed of the earth?
7.29×10-5 rad/s

(Got this one not too badly)

Assume the Earth is spherical. Relative to someone on the rotation axis, what is the linear speed of an object on the surface if the radius vector from the center of the Earth to the object makes an angle of 76.0° with the axis of rotation. The radius of the Earth is 6.37×103 km.

What is the acceleration of the object on the surface of the Earth in the previous problem?

Homework Equations



V = r ω
a = v^2/r

The Attempt at a Solution



V = r ω
(sin(76)*6370000)*(2pi/81400) = 477 m/sec
a = v^2/r
(477.089)^2/(sin(76)*6370000) = .036826 m/s^2

Apparently these are wrong. Anyone how to get to an answer here?
 
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  • #2
Where did the 81400 come from in your velocity formula?
 
  • #3
gneill said:
Where did the 81400 come from in your velocity formula?
The period of the earth
 
  • #4
Staerke said:
The period of the earth

Maybe you should check that figure. The rotation period (sidereal) is 23hr 56min 4sec.
 
  • #5
That was my issue. Thanks for the reply :)
 

1. What is the rotation of a sphere?

The rotation of a sphere refers to the motion of a sphere around its own axis. It is the spinning motion of the sphere, similar to the way the Earth rotates on its axis once every 24 hours.

2. How is the acceleration of a rotating sphere calculated?

The acceleration of a rotating sphere can be calculated using the formula a = ω²r, where a is the acceleration, ω is the angular velocity, and r is the radius of the sphere. This formula is derived from the basic physics equation for acceleration, a = v²/r, where v is the linear velocity.

3. What is the relationship between angular velocity and linear velocity?

Angular velocity and linear velocity are directly proportional to each other. This means that as the angular velocity of a rotating sphere increases, so does its linear velocity. The relationship between the two can be described by the equation v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the radius of the sphere.

4. Can the acceleration of a rotating sphere change?

Yes, the acceleration of a rotating sphere can change. This can happen if the angular velocity or the radius of the sphere changes. If the angular velocity increases, the acceleration will also increase, and vice versa. Similarly, if the radius of the sphere changes, the acceleration will also change accordingly.

5. Is the velocity of a rotating sphere constant?

No, the velocity of a rotating sphere is not constant. The linear velocity of a rotating sphere changes constantly as it moves around its axis. However, the angular velocity remains constant, unless there is a change in the radius or moment of inertia of the sphere.

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