Calculating Angular Velocity of a Rolling Sphere on an Inclined Plane

AI Thread Summary
To calculate the angular velocity of a solid sphere rolling down an inclined plane, the translational velocity must first be determined. The correct formula for translational velocity is v = d/t, where d is the distance traveled and t is the time taken. The initial calculations yielding 61 rad/s are considered too high by peers, who suggest results should be under 1 rad/s. It's essential to ensure accurate measurements of distance and time to achieve a correct angular velocity. Clarifying these values will lead to a more precise calculation.
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Homework Statement



so i need to find the angular velocity of a solid sphere rolling down an inclined plane. I know the mass, radius, and distance the sphere travels.

Homework Equations





The Attempt at a Solution



I know how to get angular velocity, but i need the translational velocity first (m/s). Do i use d=v/t or d=1/2(Vi-Vf)(t) which should go down to v=2d/t. I am getting like 61rad/s and after talking to some other people, they said that was too big. They are getting theirs to be under 1...which doesn't make sense to me
 
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and i know the time it takes. And i meant to say v=d/t above
 
i need this tonight
any help would be great!
thanks
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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