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2.5. The relationship of angular and linear quantities

Lecture



Separate points of a rotating body have different linear velocities. 2.5. The relationship of angular and linear quantities . The speed of each point, being tangential to the corresponding circle, continuously changes its direction. Speed ​​magnitude 2.5. The relationship of angular and linear quantities determined by the speed of body rotation 2.5. The relationship of angular and linear quantities and the distance R of the considered point from the axis of rotation. Let for a small period of time 2.5. The relationship of angular and linear quantities the body turned to the corner 2.5. The relationship of angular and linear quantities (figure 2.4). A point located at a distance R from the axis passes the path equal to

2.5. The relationship of angular and linear quantities

Linear velocity of a point by definition.

2.5. The relationship of angular and linear quantities (2.6)

Find the linear acceleration points of the rotating body. Normal acceleration:

2.5. The relationship of angular and linear quantities

substituting the value of speed from (2.6), we find:

2.5. The relationship of angular and linear quantities (2.7)

Tangential acceleration

2.5. The relationship of angular and linear quantities

2.5. The relationship of angular and linear quantities

Using the same relation (2.6) we get

2.5. The relationship of angular and linear quantities (2.8)

Thus, both normal and tangential accelerations grow linearly with the distance of the point from the axis of rotation.

See also

created: 2014-09-13
updated: 2026-03-09
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Lectures and tutorial on "Physical foundations of mechanics"

Terms: Physical foundations of mechanics

1. Subject mechanics. Kinematics. Introduction
1.1. The radius vector of the material point
1.2.Kinematic equations of motion of a material point
1.3. Material point trajectory
1.4.Vector movement
1.5. Material point velocity
1.6. Acceleration
1.7. Curved motion. Tangential and normal acceleration
1.8. Guidelines for solving problems in kinematics
2. Kinematics of rotational motion. Introduction
2.1. Angle of rotation of a solid body
2.3. Period and frequency of treatment
2.4. Angular acceleration
2.2. Angular velocity
2.5. The relationship of angular and linear quantities
3.1. Newton's first law
3.2. Concept of power
3.3. Weight. Newton's Second Law
3.4. The principle of independence of action of forces
3.5.Third Newton's Law
3.6 Transformation of Galilean coordinates and the mechanical principle of relativity
3.7.The basic equation of the dynamics of the translational motion of a material point. Material point impulse
3.8. Center of Inertia System
3.9. Universal form of the second law of Newton, expressed through the impulse of the system
3.10. The basic equation of the dynamics of the translational motion of a rigid body
3.11.Isolated (closed) system. Momentum conservation law
3.12. Guidelines for solving problems in dynamics
4.1. Basic concepts about the energy of a mechanical system
4.2. Mechanical work
4.3. Conservative forces. Condition of potentiality of the force field
4.4. Power
4.5 Kinetic energy
4.6.Potential energy
4.7. The law of conservation and transformation of energy
4.8. Relationship between potential energy and power
5. Dynamics of rotational motion of a rigid body. Introduction
5.1. Features of rotational motion
5.2. Torque (or moment of force)
5.3. The moment of inertia of the material point relative to a fixed axis of rotation
5.4. Moment of inertia of a solid
5.5. Newton's second law for rotational motion and its analysis
5.6. Moment of impulse of the material point and solid
5.7. The basic equation of the dynamics of rotational motion
5.8. The law of conservation of moment of momentum
5.9. Gyroscope. Gyroscopic effect
5.10. Kinetic energy of a rotating body
5.11. The work of external forces during the rotation of a solid body
6. Special theory of relativity. Introduction
6.1. Lorentz transformations
6.2. Simultaneity of events in different reference systems
6.3. The length of bodies in different systems
6.4. Duration of events in different reference systems
6.5. Relativistic law of velocity addition
6.6. Relativistic impulse