Clarification on different kinds of acceleration

[henry3369]

Homework Statement

Not a homework question, I just need clarification.
I'm slightly confused on the different kinds of accelerations involved in a rotating body. I often see three types of acceleration:
1. radial
2. tangential
3. angular

I'm assuming radial acceleration is the same as centripetal acceleration. So is tangential acceleration the same thing as the linear acceleration of the body being observed while angular acceleration is the acceleration of the rotation (which points in the same direction of the axis of rotation I believe)? Also when a question asks: What is the resultant acceleration of the rotating body, what am I solving for?

 

[gneill]

Homework Statement

Not a homework question, I just need clarification.
I'm slightly confused on the different kinds of accelerations involved in a rotating body. I often see three types of acceleration:
1. radial
2. tangential
3. angular

I'm assuming radial acceleration is the same as centripetal acceleration. So is tangential acceleration the same thing as the linear acceleration of the body being observed while angular acceleration is the acceleration of the rotation (which points in the same direction of the axis of rotation I believe)?

Yes, you have it right. The angular acceleration vector lies along the rotation axis and its direction is usually assessed by way of the right hand rule (for right-handed coordinate systems).

Also when a question asks: What is the resultant acceleration of the rotating body, what am I solving for?

This can sometimes be context dependent, but generally it refers to the total acceleration felt by the body. If you were to draw a Free Body Diagram for the body, it would be sum of all the accelerations acting on it.

 

[henry3369]

Yes, you have it right. The angular acceleration vector lies along the rotation axis and its direction is usually assessed by way of the right hand rule (for right-handed coordinate systems).

This can sometimes be context dependent, but generally it refers to the total acceleration felt by the body. If you were to draw a Free Body Diagram for the body, it would be sum of all the accelerations acting on it.

So is linear acceleration the same as tangential acceleration?

 

[henry3369]

Yes, you have it right. The angular acceleration vector lies along the rotation axis and its direction is usually assessed by way of the right hand rule (for right-handed coordinate systems).

This can sometimes be context dependent, but generally it refers to the total acceleration felt by the body. If you were to draw a Free Body Diagram for the body, it would be sum of all the accelerations acting on it.

Or is tangential acceleration a component of linear acceleration?

 

[PhanthomJay]

Homework Statement

Not a homework question, I just need clarification.
I'm slightly confused on the different kinds of accelerations involved in a rotating body. I often see three types of acceleration:
1. radial
2. tangential
3. angular

I'm assuming radial acceleration is the same as centripetal acceleration.

yes

So is tangential acceleration the same thing as the linear acceleration of the body being observed

in a direction tangent to the curve

while angular acceleration is the acceleration of the rotation (which points in the same direction of the axis of rotation I believe)?

yes[, using right hand rule

Also when a question asks: What is the resultant acceleration of the rotating body, what am I solving for?

for pure rotation, the resultant of the tangential and radial accelerations

 

[brainpushups]

For rotational motion it is convenient to break the vectors into radial and tangential components rather than x and y components (in a plane). If something is forced to rotate around a point with its radius fixed then there is a centripetal acceleration that points inward; this acceleration just serves to change the direction of motion. A tangential acceleration in this case will result in a change in speed.

 

[PhanthomJay]

Or is tangential acceleration a component of linear acceleration?

it is not a component

So is linear acceleration the same as tangential acceleration?

the term 'linear acceleration' is most often used in reference to translational acceleration of the center of mass along a straight line, but I suppose it's ok to refer to tangential acceleration as linear acceleration of a particle at any point on the curved path, noting that it's direction is always tangent to the curve.