Characteristics of a rigid body.

  • Thread starter Thread starter andyrk
  • Start date Start date
  • Tags Tags
    Body Rigid body
Click For Summary
SUMMARY

The discussion centers on the characteristics of rigid bodies, specifically addressing why angular velocity and angular acceleration are uniform across all points on a rigid body. It is established that if a rigid body rotates, the angles defined by three points A, B, and C remain constant, leading to the conclusion that the angular velocities of points A, B, and C must be equal. The conversation emphasizes that any variation in velocity between points would contradict the definition of a rigid body, as it would imply deformation.

PREREQUISITES
  • Understanding of rigid body dynamics
  • Familiarity with angular velocity and angular acceleration concepts
  • Basic knowledge of rotational motion
  • Comprehension of geometric relationships in three-dimensional space
NEXT STEPS
  • Study the principles of rigid body dynamics in classical mechanics
  • Learn about the mathematical representation of angular velocity
  • Explore the implications of non-rigid body motion in physics
  • Investigate the relationship between linear and angular motion
USEFUL FOR

This discussion is beneficial for physics students, mechanical engineers, and anyone interested in the principles of rotational dynamics and the behavior of rigid bodies in motion.

andyrk
Messages
658
Reaction score
5
Why is the angular velocity and angular acceleration(if the rigid body has some) same for all points on a rigid body?
 
Physics news on Phys.org
What would happen if the front and back of a car had different velocity?
 
Take an angle fixed by three points A, B, C within the body. As the body rotates, the angle ABC must be preserved. So AB and BC must rotate by the same angle. Differentiating, deduce that the angular velocities and accelerations must also be the same.
 
  • Like
Likes   Reactions: 1 person
haruspex said:
Take an angle fixed by three points A, B, C within the body. As the body rotates, the angle ABC must be preserved. So AB and BC must rotate by the same angle. Differentiating, deduce that the angular velocities and accelerations must also be the same.

But this gets that angular velocity of AB=angular velocity of BC
How does this get that angular velocity of A,B,C are equal?
 
Hint: look up the definition of 'rigid'.
 
The points are arbitrary. So the centre of rotation can be B. That means the angular velocity of A is the same as the angular velocity of AB...

Angular velocity of A = Angular velocity of AB = Angular velocity of CB = Angular velocity of C

It's why I asked the question above. If two points on a body have different velocity (angular or linear) then those points must get closer together or further apart which would imply it's not a rigid body.
 

Similar threads

Problem in understanding angular momentum of a rigid body
  • · Replies 10 ·
Replies
10
Views
2K
Stability of rigid body rotation about different axes
  • · Replies 5 ·
Replies
5
Views
2K
Question on Moment of Inertia Tensor of a Rotating Rigid Body
  • · Replies 4 ·
Replies
4
Views
2K
When are reactive forces enough to support this body?
  • · Replies 14 ·
Replies
14
Views
1K
Kinetic energy of a composite body
  • · Replies 11 ·
Replies
11
Views
2K
Rod with Current on Rails in Magnetic Field
  • · Replies 12 ·
Replies
12
Views
2K
What does it mean that a rigid body is in equilibrium?
  • · Replies 3 ·
Replies
3
Views
2K
2 bodies spining and cut in the middle
  • · Replies 16 ·
Replies
16
Views
2K
Conservation of Linear Momentum of Rigid Body
  • · Replies 3 ·
Replies
3
Views
2K
Where on a rigid body is a resultant force applied?
  • · Replies 11 ·
Replies
11
Views
2K