Rotation of sphere problem, acceleration and velocity

AI Thread Summary
The discussion revolves around calculating the angular speed, linear speed, and acceleration of an object on Earth's surface based on its rotation. The angular speed of Earth is confirmed as 7.29×10^-5 rad/s. A user attempts to calculate the linear speed using the formula V = r ω but encounters confusion regarding the use of 81400 in their calculations. It is clarified that the correct period for Earth's rotation is 23 hours 56 minutes and 4 seconds, which resolves the issue. The conversation emphasizes the importance of accurate values in physics calculations.
Staerke
Messages
12
Reaction score
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?
 
Physics news on Phys.org
Where did the 81400 come from in your velocity formula?
 
gneill said:
Where did the 81400 come from in your velocity formula?
The period of the earth
 
Staerke said:
The period of the earth

Maybe you should check that figure. The rotation period (sidereal) is 23hr 56min 4sec.
 
That was my issue. Thanks for the reply :)
 
Thread 'Voltmeter readings for this circuit with switches'

Thread 'Voltmeter readings for this circuit with switches'

TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...
View full post »
Thread 'Struggling to make relation between elastic force and height'

Thread 'Struggling to make relation between elastic force and height'

Hello guys this is what I tried so far. I used the UTS to calculate the force it needs when the rope tears. My idea was to make a relationship/ function that would give me the force depending on height. Yeah i couldnt find a way to solve it. I also thought about how I could use hooks law (how it was given to me in my script) with the thought of instead of having two part of a rope id have one singular rope from the middle to the top where I could find the difference in height. But the...
View full post »

Similar threads

Calculate the magnetic moment of a rotating sphere
Replies
17
Views
2K
Is My Calculation of Centripetal Acceleration and Tangential Velocity Correct?
Replies
12
Views
1K
Conservation of energy problem: Ball rolling down inclined plane and then through a loop-the-loop
Replies
10
Views
2K
Period and Velocity of Oscillating Sphere Attached to Spring
Replies
10
Views
2K
Calculating tangential acceleration of rotating object
Replies
2
Views
3K
Another rotation problem -- Acceleration of a ring rolling on a surface
Replies
1
Views
743
Wooden sphere rolling on a double metal track
2
Replies
97
Views
5K
What is the angle between the acceleration and velocity when rotating?
Replies
13
Views
2K
System of two wheels of different sizes with an axle through their centers
2
Replies
67
Views
4K
Two masses on a rotating platform
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top