Circular Motion and Gravitation
Circular Motion and Gravitation
Circular motion is everywhere, from atoms to galaxies, from flagella to Ferris wheels. Two terms are frequently used to describe such motion. In general, we say that an object rotates when the axis of rotation lies within the body, and that it revolves when the axis is outside it. Thus, the Earth rotates on its axis and revolves about the Sun.
When a body rotates on its axis, all the particles of the body revolve – that is, they move in circular paths about the body’s axis of rotation. For example, the particles that make up a compact disc all travel in circles about the hub of the CD player. In fact, as a “particle” on Earth, you are continually in circular motion about the Earth’s rotational axis.
Gravity plays a large role in determining the motions of the planets, since it supplies the force necessary to maintain their nearly circular orbits. Newton’s Law of Gravity describes this fundamental force and will analyze the planetary motion in terms of this and other related basic laws. The same considerations will help you understand the motions of Earth satellites, of which there is one natural one and many artificial ones.
Angular Measure
Motion is described as a time rate of change of position. Angular velocity involves a time rate of change of position, which is expressed by an angle. It is important to be able to relate the angular description of circular motion to the orbital or tangential description, that is, to relate the angular displacement to the arc length s. The arc length is the distance traveled along the circular path and the angle θ is said to subtend (define) the arc length. A unit that is very convenient for relating angle to the arc length is the radian (rad), which is defined as the angle subtending an arc length (s) that is equal to the radius (r).
2π rad=360°
1 rad=360°2π=57.3°
The number of radians subtended by an arbitrary arc length is equal to the number of radii that
Circular motion is everywhere, from atoms to galaxies, from flagella to Ferris wheels. Two terms are frequently used to describe such motion. In general, we say that an object rotates when the axis of rotation lies within the body, and that it revolves when the axis is outside it. Thus, the Earth rotates on its axis and revolves about the Sun.
When a body rotates on its axis, all the particles of the body revolve – that is, they move in circular paths about the body’s axis of rotation. For example, the particles that make up a compact disc all travel in circles about the hub of the CD player. In fact, as a “particle” on Earth, you are continually in circular motion about the Earth’s rotational axis.
Gravity plays a large role in determining the motions of the planets, since it supplies the force necessary to maintain their nearly circular orbits. Newton’s Law of Gravity describes this fundamental force and will analyze the planetary motion in terms of this and other related basic laws. The same considerations will help you understand the motions of Earth satellites, of which there is one natural one and many artificial ones.
Angular Measure
Motion is described as a time rate of change of position. Angular velocity involves a time rate of change of position, which is expressed by an angle. It is important to be able to relate the angular description of circular motion to the orbital or tangential description, that is, to relate the angular displacement to the arc length s. The arc length is the distance traveled along the circular path and the angle θ is said to subtend (define) the arc length. A unit that is very convenient for relating angle to the arc length is the radian (rad), which is defined as the angle subtending an arc length (s) that is equal to the radius (r).
2π rad=360°
1 rad=360°2π=57.3°
The number of radians subtended by an arbitrary arc length is equal to the number of radii that