Tangential Acceleration vs. Tangential component of force

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SUMMARY

The discussion focuses on calculating the tangential component of force for a ball moving in a circular path with a radius of 5 meters and an angular acceleration of 2.09 rad/s². The tangential acceleration is determined to be 10.47 m/s², leading to a calculated tangential force of 1.3 N. However, the error arises from the inclusion of the unit vector in the final force expression, which should be omitted. The correct representation of the tangential component of force is simply 1.3 N.

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  • Knowledge of Newton's second law of motion
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Homework Statement


A ball moves counterclockwise in a circle and is speeding up. The radius of the circle is 5 m.

Its angular acceleration is α, (2.09 rad/s2)[tex]\hat{k}[/tex]

The ball's mass is 0.125 kg.

What is the tangential component of the force on the particle?

Homework Equations


The Attempt at a Solution


So the tangential acceleration is at = αr = 10.47 m/s2[tex]\hat{t}[/tex]

(Define [tex]\hat{t}[/tex] to be tangent to the circle. At the top of the circle, it points to the left. At the bottom, it points to the right and so on).

Then the tangential component of the FORCE on this particle should be (10.47 m/s2)[tex]\hat{t}[/tex] * 0.125 kg = (1.3 N)[tex]\hat{t}[/tex]

But I got it wrong, and I have no clue why. Can anyone help me out? I got half the marks so it may just be a small error somewhere =\
 
Last edited:
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The calculation looks OK. Components of vectors do not have unit vectors attached to them. Try without the t-hat.
 

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