Radial Acceleration in cylindrical coordinates

Thread starter VooDoo
Start date Apr 4, 2008
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Acceleration Coordinates Cylindrical Cylindrical coordinates Radial Radial acceleration

In summary, radial acceleration in cylindrical coordinates is a measure of an object's change in velocity perpendicular to the axis of rotation, calculated using the formula a<sub>r</sub> = v<sup>2</sup>/r. It is different from tangential acceleration, which is directed tangent to the object's motion. Radial acceleration and angular velocity are directly related, with an increase in angular velocity resulting in an increase in radial acceleration. Radial acceleration is crucial in keeping an object moving in a circular path, and it can be negative if the object is slowing down or moving in the opposite direction of the axis of rotation.

Apr 4, 2008

VooDoo

Hey guys,

Been given this formula for radial acceleration, I am not sure how they derived it. I have tried but the only forumla I know is a(radial) = v^2/r

[tex]A_{r}[/tex] = [tex]\ddot{r}[/tex] - r[tex]\dot{\theta}^{2}[/tex]EDIT - should be minus not plus

Last edited: Apr 4, 2008

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Apr 5, 2008

tiny-tim

Science Advisor

Homework Helper

Hi VooDoo!

They differentiated r.(cosθ.x + sinθ.y), twice!

1. What is radial acceleration in cylindrical coordinates?

Radial acceleration in cylindrical coordinates is a measure of the rate at which an object's velocity is changing in the direction perpendicular to the axis of rotation. It is also known as centripetal acceleration and is calculated using the formula a_r = v²/r, where v is the velocity of the object and r is the radius of the cylindrical coordinate system.

2. How is radial acceleration different from tangential acceleration?

Radial acceleration and tangential acceleration are both components of an object's total acceleration in cylindrical coordinates. Radial acceleration is directed towards or away from the axis of rotation, while tangential acceleration is directed tangent to the path of the object's motion. Tangential acceleration is calculated using the formula a_t = d(v)/dt, where v is the object's velocity and t is time.

3. What is the relationship between radial acceleration and angular velocity?

Radial acceleration and angular velocity are directly related in cylindrical coordinates. As the angular velocity of an object increases, its radial acceleration also increases. This is because a higher angular velocity means the object is moving faster along its circular path, resulting in a larger change in velocity over a given time period and thus a larger radial acceleration.

4. How does radial acceleration affect an object's motion?

Radial acceleration plays a crucial role in an object's motion in cylindrical coordinates. It is responsible for keeping the object moving in a circular path, as it constantly changes the direction of the object's velocity towards the center of rotation. Without radial acceleration, the object would continue moving in a straight line tangent to its circular path.

5. Can radial acceleration be negative?

Yes, radial acceleration can be negative. This occurs when an object is slowing down while moving in a circular path or when it is moving in the opposite direction of the axis of rotation. In these cases, the direction of the object's velocity and the direction of the radial acceleration are opposite, resulting in a negative value for the radial acceleration.