Tangential acceleration - radial acceleration

AI Thread Summary
In a circular motion scenario on a frictionless table, the tangential acceleration is zero when the tangential velocity is constant, as there is no change in speed. The correct formula for radial acceleration is V^2 / r, where V is the tangential velocity and r is the radius. To calculate angular acceleration, the formula is α = dω/dt, which relates to the change in angular velocity over time. The discussion clarifies the confusion between tangential velocity and radial acceleration, emphasizing that tangential acceleration only occurs with a change in speed. Overall, the key takeaway is that with constant tangential velocity, tangential acceleration remains zero.
finitefemmet
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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 alot!

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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