Linear/Angular Velocity and Acceleration

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The discussion revolves around calculating the angular and linear velocities, as well as the angular and linear accelerations of a point on a rotating sphere. The sphere has a fixed angular velocity, and the problem requires understanding the relationship between angular and linear measures. Participants express confusion regarding how to approach the problem, particularly whether to consider the longitude (phi) in calculations since the distance from the center remains constant. Clarification on the formulas and concepts related to angular motion is sought to effectively solve the homework problem. Understanding these relationships is crucial for accurately determining the required velocities and accelerations.
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Homework Statement



A sphere of radius r0 is rotating about an axis through its geometric center with fixed angular velocity Ω0. Measuring latitude and longitude as is done for the Earth, what is the angular velocity of a point at Θ0 degrees North and Φ0 degrees East.
What is the linear velocity?
What is the angular acceleration?
What is the linear acceleration?

Homework Equations



I don't understand the relationships between angular and linear or how to begin to set this one up.
 
Last edited:
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can you negate phi since your distance from the center of the sphere doesn't change at all?
 
Can anyone offer any help on this?
 
Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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