Tangential acceleration - radial acceleration

In summary, for a ball in circular motion on a frictionless table with a constant tangential velocity, the tangential acceleration is always zero and the formula for radial acceleration is alpha = d(omega)/dt = d^2(theta)/dt^2. For tangential acceleration, the formula is a = d(v)/dt = d^2(r)/dt^2.
  • #1
finitefemmet
13
0
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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  • #2
The tangential accelearation of a constant tangential velocity is always zero, because the change in velocity is zero. The formula for radial part is:
[itex] \alpha = \dfrac{\text{d}\omega}{\text{d}t} = \dfrac{\text{d}^2\theta}{\text{d}t^2}[/itex]
And for tangential :
[itex] \vec{a} = \dfrac{\text{d}\vec{v}}{\text{d}t} = \dfrac{\text{d}^2\vec{r}}{\text{d}t^2}[/itex]
 
  • #3
Thanks that solved it for me;)
 

1. What is tangential acceleration?

Tangential acceleration is the rate of change of an object's tangential velocity. It is the component of acceleration that is parallel to the object's instantaneous direction of motion.

2. What is radial acceleration?

Radial acceleration is the component of acceleration that is directed towards the center of a curved path. It is perpendicular to the tangential acceleration and is responsible for keeping an object moving in a curved path.

3. How are tangential and radial acceleration related?

Tangential and radial acceleration are related through the formula for total acceleration, which is the vector sum of the two components. They are also related to each other through the radius of curvature of the object's path. As the radius of curvature decreases, the tangential acceleration increases and the radial acceleration decreases.

4. What is the difference between tangential acceleration and centripetal acceleration?

Tangential acceleration is the component of acceleration that is parallel to the object's instantaneous direction of motion, while centripetal acceleration is the component of acceleration that is directed towards the center of a curved path. Centripetal acceleration is a type of radial acceleration, but radial acceleration can also exist in other directions besides towards the center.

5. How is tangential acceleration calculated?

Tangential acceleration can be calculated using the formula a = v^2/r, where v is the tangential velocity and r is the radius of curvature of the object's path. It can also be calculated using the derivative of the tangential velocity with respect to time, a = dv/dt.

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