Angular Acceleration vs Tangential Acceleration

Click For Summary

Discussion Overview

The discussion revolves around the differences between angular acceleration and tangential acceleration, particularly in the context of forces applied to a rotating object. Participants explore the implications of fixed and non-fixed mass points, torque, and the relationship between angular and tangential velocities and accelerations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses uncertainty about how a force applied to a rotating object affects angular acceleration.
  • Another participant states that a force producing torque about the center of mass will result in angular acceleration while also causing translational acceleration of the center of mass.
  • A different viewpoint suggests that if the mass is fixed at a point, the force will only produce angular acceleration, whereas if the mass is not fixed, both rotational and translational movements occur.
  • One participant explains that as a force is applied, the angle of rotation increases, leading to angular velocity and angular acceleration, while noting that different points on the object will have varying tangential velocities based on their distance from the center of rotation.
  • Another participant clarifies that if there is a fixed axis of rotation, the force creates a constant torque, resulting in constant angular acceleration, with tangential acceleration depending on the distance from the axis.

Areas of Agreement / Disagreement

Participants express differing views on the effects of fixed versus non-fixed mass points on angular and tangential acceleration. There is no consensus on the implications of these conditions, and the discussion remains unresolved regarding the nuances of these concepts.

Contextual Notes

Participants reference the need for clarity on whether the mass is fixed or not, which affects the resulting accelerations. The discussion also touches on the dependence of tangential acceleration on the radius from the axis of rotation.

Telanor
Messages
3
Reaction score
0
Im a little fuzzy on the difference between the two. If you look at the attached picture, if that force stays with the object as it rotates, like a hand pushing in the same spot, would that force cause an angular acceleration?
 

Attachments

  • illistration.JPG
    illistration.JPG
    3.9 KB · Views: 1,239
Physics news on Phys.org
Since the force exerts a torque about the object's center of mass, it will produce an angular acceleration about the center of mass. The force will also produce an acceleration of the object's center of mass.
 
Hey Telanor,

If the mass was fixed where represented by the point in your diagram, then the force will only produce angular acceleration, as a constant force will produce acceleration around that point.

If the mass isn't fixed, the mass will exhibit both rotational and translational movement and acceleration.
 
Ok, let's keep things simple. Way more simple. Draw a line on the box. That line will rotate an angle theta as you apply the force. That angle will get bigger and biger as you keep on applying the force. The rate at which that angle gets bigger is the angluar velocity. Same deal for the angular acceleration.

NOW, each point on the body will have a DIFFERENT tangential velocity. It will depend on how far out it is-i.e. the radius. At the very center of rotation, the tangential velocity will be zero. As you move further out, it will increase. This is because it is proportional to radius.

Consider this. All points on the body are rigid. As it sweeps an angle, let's say theta, all the points rotate. But the points on the OUTTER most edge must sweep a BIGGER circle in the same amount of time, hence they must have a higher TANGENTIAL acceleration.
 
If that dot in the center of your diagram represents a fixed axis about which the object is free to rotate (no friction, of course), then it's a much simpler situation. (You didn't mention any fixed axis in your original post.)

In that case the force exerts a constant torque about the center, which produces a constant angular acceleration. The tangential acceleration of each point of the object depends on its distance from the axis: [itex]a_t = \alpha r[/itex].
 

Similar threads

Undergrad Conservation of angular momentum in the iceskater example
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Why is there angular acceleration in a non-spinning gyroscope?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Mechanics of an inertial balance
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad I'm calculating more energy out than I put in
  • · Replies 138 ·
5
Replies
138
Views
9K
Undergrad Spinning objects and angular acceleration
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Translational + Angular Acceleration of Free Body (not fixed)
  • · Replies 14 ·
Replies
14
Views
3K
High School The physics of flywheel launchers (like tennis ball shooters)
  • · Replies 60 ·
3
Replies
60
Views
7K
High School Sign conventions in torque and non-uniform circular motion
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Angular Momentum problem v2 (mass moving inward or outward)
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Rotating Sphere: Conceptual Question
  • · Replies 10 ·
Replies
10
Views
3K