What is the tangential acceleration?

AI Thread Summary
Tangential acceleration is the rate of change of tangential velocity in circular motion. In the given scenario, a 2.5kg ball revolves in a circle with a radius of 0.9m and a speed of 7m/s, at an angle of 60 degrees below the horizontal. The discussion highlights confusion regarding the application of forces, such as centripetal and gravitational forces, in calculating tangential acceleration. Participants suggest using the equation a = v²/r for clarity, while emphasizing the importance of understanding the forces acting on the ball. Overall, the relationship between the angle, mass, and the forces involved in circular motion remains a central point of inquiry.
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Homework Statement


a ball of 2.5kg revolves in a circle on a string with a radius of 0.9m. at the moment when the string makes an angle of 60 degrees below the horizontal, the ball's speed is 7m/s. at this specific point, what is the tangential acceleration?

Homework Equations


A_t = r*angular acceleration
A_t = dv/dt

The Attempt at a Solution


I understand what tangential acceleration is and how to calculate it when a time interval is given. However, this scenario doesn't make much sense, and I can't find an equation to use that I could plug in some of my data. I know m*g*cos60 is the gravitational acceleration component that is tangent to the ball's circular rotation at that point in time, but that answer didn't work for tangential acceleration.

Homework Statement


Homework Equations


The Attempt at a Solution

 
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Think in terms of forces.
 
i understand there are forces, including centripetal force and gravitational force. but i do not understand how they directly relate to tangential acceleration.
 
I presume the circular motion is in a vertical plane.
Where the **** did you get cos(21) from?
 
Suggest you do a drawing and consider which forces contribute to tangential acceleration and which don't.
 
Can you just use: a = v2/r

Or does it help in any way? I'm not sure where the mass and angle is coming into this if its rotating on a horizontal plane.
 
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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