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Questions and Answers
What defines a rigid body in terms of particle distance?
What defines a rigid body in terms of particle distance?
- Distances between particles increase as external force is applied.
- Particles can move independently of each other.
- Distances between particles fluctuate significantly over time.
- Distance between each pair of particles remains constant. (correct)
When does a system behave like a non-rigid body?
When does a system behave like a non-rigid body?
- When the relative distances change due to external impact. (correct)
- When all particles are in uniform circular motion.
- When there is no distance change between particles.
- When external forces are not applied.
In a rigid body, how does the motion of point B relate to point A?
In a rigid body, how does the motion of point B relate to point A?
- B moves faster than A at all times.
- It can lead to separate linear velocities.
- There is no motion between A and B.
- It is circular and perpendicular to the line joining A and B. (correct)
Which of the following statements about a rigid body is incorrect?
Which of the following statements about a rigid body is incorrect?
How does the velocity of approach or separation behave in a rigid body?
How does the velocity of approach or separation behave in a rigid body?
What happens to the behavior of a rigid body when one particle has a different angular velocity than another?
What happens to the behavior of a rigid body when one particle has a different angular velocity than another?
Which of the following scenarios defines a rigid body system?
Which of the following scenarios defines a rigid body system?
What will occur if the conditions of rigidity are violated in a system?
What will occur if the conditions of rigidity are violated in a system?
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Study Notes
Rigid Body Definition
- A rigid body is a system of particles where the distance between each pair of particles remains constant over time.
- Rigid bodies are a mathematical concept; any system that meets this criterion is considered rigid.
Characteristics of Rigid Bodies
- The shape and size of a rigid system remain constant since there is no change in the relative distances between particles.
- Examples of rigid bodies include stones and cricket balls, whereas balloons and elastic strings are typically non-rigid.
- When external forces alter the relative distances (e.g., when a bat hits a cricket ball), the system behaves as non-rigid.
Relative Motion in Rigid Bodies
- In a rigid body, there is no velocity of separation or approach between any pair of particles.
- The motion of one particle relative to another is circular; thus, any relative motion is perpendicular to the line joining the two particles.
Circular Motion and Velocity
- Velocities of particles A and B, with respect to the ground, are denoted as VA and VB.
- For a rigid body: ( VA \cos \theta_1 = VB \cos \theta_2 ) indicates there is no relative velocity of approach or separation.
Non-Rigid vs. Rigid Systems
- In a non-rigid system, the velocities of particles may not be equal (e.g., ( vA \neq vB )).
- A system consisting of particles A and B can be rigid while including additional elements (like a ring) can turn it non-rigid.
Angular Velocity
- In any rigid body, the angular velocity remains constant for all points in the body.
- For three particles in a rigid system (A, B, C), all sides must rotate through the same angle during motion.
- Angular velocities are denoted as ( \omega ), showing the same angular velocity between any two particles relative to a third point.
Summary of Motion Dynamics
- A rigid body's particles have synchronized motion characterized by uniform angular velocity.
- When observing the motion, each particle appears to move in a circular path relative to other particles in the rigid structure.
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