Linear/Angular Velocity and Acceleration

AI Thread Summary
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 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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