helical motion

Examples of helical motion in the following topics:

• Helical Motion

  • Helical motion results when the velocity vector is not perpendicular to the magnetic field vector.
  • In the section on circular motion we described the motion of a charged particle with the magnetic field vector aligned perpendicular to the velocity of the particle.
  • This produces helical motion (i.e., spiral motion) rather than a circular motion.
  • Uniform circular motion results.
  • Describe conditions that lead to the helical motion of a charged particle in the magnetic field

• Direction of the Magnetic Force: The Right Hand Rule

  • Because the force is always perpendicular to the velocity vector, a pure magnetic field will not accelerate a charged particle in a single direction, however will produce circular or helical motion (a concept explored in more detail in future sections).

• Springs

  • Neglecting frictional forces, Mechanical energy conservation demands that, at any point during its motion,$\begin{aligned} Total ~Energy &= \frac{1}{2} m v^2 + \frac{1}{2}k x^2 \\ &= \frac{1}{2} k x_f^2 = constant.
  • Plot of applied force F vs. elongation X for a helical spring according to Hooke's law (solid line) and what the actual plot might look like (dashed line).

• Electric vs. Magnetic Forces

  • Force due to both electric and magnetic forces will influence the motion of charged particles.
  • The angle dependence of the magnetic field also causes charged particles to move perpendicular to the magnetic field lines in a circular or helical fashion, while a particle in an electric field will move in a straight line along an electric field line.
  • A further difference between magnetic and electric forces is that magnetic fields do not net work, since the particle motion is circular and therefore ends up in the same place.
  • We mentioned briefly above that the motion of charged particles relative to the field lines differs depending on whether one is dealing with electric or magnetic fields.

• Defining Kinematics

  • Kinematics is the study of the motion of points, objects, and groups of objects without considering the causes of its motion.
  • Kinematics is the branch of classical mechanics that describes the motion of points, objects and systems of groups of objects, without reference to the causes of motion (i.e., forces).
  • The study of kinematics is often referred to as the "geometry of motion."
  • Objects are in motion all around us.
  • The word "kinematics" comes from a Greek word "kinesis" meaning motion, and is related to other English words such as "cinema" (movies) and "kinesiology" (the study of human motion).

• Circular Motion

  • Uniform circular motion describes the motion of an object along a circle or a circular arc at constant speed.
  • It is the basic form of rotational motion in the same way that uniform linear motion is the basic form of translational motion.
  • However, the two types of motion are different with respect to the force required to maintain the motion.
  • Let us consider Newton's first law of motion.
  • Therefore, uniform linear motion indicates the absence of a net external force.

• Overview of Non-Uniform Circular Motion

  • Non-uniform circular motion denotes a change in the speed of a particle moving along a circular path.
  • What do we mean by non-uniform circular motion?
  • The answer lies in the definition of uniform circular motion, which is a circular motion with constant speed.
  • The circular motion adjusts its radius in response to changes in speed.
  • In non-uniform circular motion, the magnitude of the angular velocity changes over time.

• Constant Acceleration

  • Analyzing two-dimensional projectile motion is done by breaking it into two motions: along the horizontal and vertical axes.
  • Projectile motion is the motion of an object thrown, or projected, into the air, subject only to the force of gravity.
  • The motion of falling objects is a simple one-dimensional type of projectile motion in which there is no horizontal movement.
  • The key to analyzing two-dimensional projectile motion is to break it into two motions, one along the horizontal axis and the other along the vertical.
  • We analyze two-dimensional projectile motion by breaking it into two independent one-dimensional motions along the vertical and horizontal axes.

• Motion Diagrams

  • A motion diagram is a pictorial description of an object's motion and represents the position of an object at equally spaced time intervals.
  • A motion diagram is a pictorial description of the motion of an object.
  • For this reason, a motion diagram is more information than a path diagram.
  • is a motion diagram of a simple trajectory.
  • Motion diagram of a puck sliding on ice.

• Simple Harmonic Motion and Uniform Circular Motion

  • Simple harmonic motion is produced by the projection of uniform circular motion onto one of the axes in the x-y plane.
  • Uniform circular motion describes the motion of a body traversing a circular path at constant speed.
  • There is an easy way to produce simple harmonic motion by using uniform circular motion.
  • The next figure shows the basic relationship between uniform circular motion and simple harmonic motion.
  • Describe relationship between the simple harmonic motion and uniform circular motion