Rotational Motion

Introduction

As objects rotate they have an angular velocity. This implies that there is an additional form of kinetic energy, rotational kinetic energy. So, an object can have kinetic energy due to linear motion, kinetic energy due to rotational motion, or both. For example a tire rolling forward would have both linear and rotational kinetic energy. Rotating objects also have angular momentum, that is momentum due to rotation. However, unlike linear momentum, the conservation of angular momentum can be applied to a single object as it changes its mass distribution. Finally, the module will touch on Kepler's laws of planetary motion. Applying the concept of rotational motion the motion of orbital bodies.

Essential Questions

How can conservation of energy be applied to fixed-axis rotation problems?
How can the relationship between linear and angular quantities for an object of circular cross-section that rolls without slipping along a fixed axis be applied?
How can the equations for translational and rotational motion be applied simultaneously to analyze rolling without slipping?
How can the total kinetic energy of an object undergoing both translational and rotational motion be calculated, and how can conservation of energy be applied to this situation?
How can the angular momentum vector for a moving particle be calculated?
How can the angular momentum vector for a rotating rigid object be calculated?
What are the conditions under which the law of conservation of angular momentum is applicable?
What is the relationship between net external torque and angular momentum?
How is angular momentum conserved when the moment of inertia of an object changes as it rotates?
What is the result of a collision between a moving particle and a rigid object that can rotate about an axis?
For an object in circular orbit, how does the velocity, period of revolution, and acceleration depend on the radius?
How is Kepler's Third Law derived for an object in circular orbit?
What is the relationship between kinetic, potential, and total energy for an object in a circular orbit?
What are Kepler's three laws and how can they be used to describe the motion of an object in an elliptical orbit?
How can the conservation of angular momentum be applied to determine the velocity and radial distance at any point in an orbit?
How can the conservation of angular momentum and conservation of energy be used to relate the speed of an object at the two extremes of an elliptical orbit?
How can energy conservation be used to analyze the motion of an object moving straight away from or straight toward a planet?

Key Terms

Angular Momentum - The quantity of rotation of a body, which is a product of its moment of inertia and its angular velocity.
Aphelion - The point where a planet is furthest from the Sun in its orbit.
Kepler's First Law of Planetary Motion - Each planet's orbit about the Sun is an ellipse.
Kepler's Second Law of Planetary Motion - An imaginary line joining a planet and Sun sweeps out an equal area of space in equal amounts of time.
Kepler's Third Law of Planetary Motion - The squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axis of their orbits.
Perihelion - The point where a planet is nearest to the Sun in its orbit.
Rotational Kinetic Energy - The energy due to the rotation of an object.

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