Tangential acceleration - radial acceleration

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SUMMARY

The discussion focuses on calculating tangential and radial acceleration for an object in uniform circular motion. The radius is 0.4m and the constant tangential velocity is 0.50m/s. It is established that the radial acceleration can be calculated using the formula V^2 / r, while the tangential acceleration is zero due to the constant tangential velocity. The angular acceleration is defined as α = dω/dt = d²θ/dt², confirming that no change in velocity results in zero tangential acceleration.

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Hi,

I got a ball in a circualar motion on a frictionless table and in a uniform circle.
I need to calculate the tangential acceleration and radial acceleration.

What I know:

Radius: 0.4m
Tangential velocity: 0.50m/s^-1 (constant)Are theese formulas right for this problem?

Radial acceleration = V^2 / r

Tangential acceleration = r*angular accelerationBecause I am confused when I mix tangential velocity with radial acceleration and so on.. and I need some help on how I can calculate the angula acceleration for the tangential acceleration.Every bit of information would help a lot!

Thanks
 
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The tangential accelearation of a constant tangential velocity is always zero, because the change in velocity is zero. The formula for radial part is:
\alpha = \dfrac{\text{d}\omega}{\text{d}t} = \dfrac{\text{d}^2\theta}{\text{d}t^2}
And for tangential :
\vec{a} = \dfrac{\text{d}\vec{v}}{\text{d}t} = \dfrac{\text{d}^2\vec{r}}{\text{d}t^2}
 
Thanks that solved it for me;)
 

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