Rotational kinematics of a ball

AI Thread Summary
A ball attached to a string experiences constant angular acceleration while moving in a horizontal circle with a radius of 0.30 m. After 0.65 seconds, its angular speed reaches 9.7 rad/s. The tangential acceleration is calculated to be 15 m/s², and the centripetal acceleration is found to be 32.3 m/s². However, there is confusion regarding the calculation of total acceleration. Clarification and assistance are requested for determining the total acceleration at t = 0.30 s.
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Homework Statement



A ball attached to a string starts at rest and undergoes a constant angular acceleration as it
travels in a horizontal circle of radius 0.30 m. After 0.65 sec, the angular speed of the ball is 9.7
rad/s. Determine the magnitudes of the ball’s tangential, centripetal, and total acceleration at
t = 0.30 s.


Homework Equations





The Attempt at a Solution


at=w-wo/t = 9.7/.65 =15 15(.30)=4.5m/s^2

which is correct. for ac I did 9.7/.3= 32.3 32.3(.65)= 21 21(.3)= 6.3


Is this correct?

NOt sure were to start for a?

Any help would be awesome.
 
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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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