straight-line motion

Examples of straight-line motion in the following topics:

• Constant Velocity Produces a Straight-Line

  • If a charged particle's velocity is parallel to the magnetic field, there is no net force and the particle moves in a straight line.
  • Recall Newton's first law of motion.
  • Because velocity is a vector, the direction remains unchanged along with the speed, so the particle continues in a single direction, such as with a straight line.
  • In this case a charged particle can continue with straight-line motion even in a strong magnetic field.
  • Identify conditions required for the particle to move in a straight line in the magnetic field

• Instananeous Velocity: A Graphical Interpretation

  • Typically, motion is not with constant velocity nor speed.
  • A graphical representation of our motion in terms of distance vs. time, therefore, would be more variable or "curvy" rather than a straight line, indicating motion with a constant velocity as shown below.
  • (We limit our discussion to one dimensional motion.
  • One way is to look at our instantaneous velocity , represented by one point on our curvy line of motion graphed with distance vs. time.
  • Motion is often observed with changing velocity.

• Angular vs. Linear Quantities

  • Linear motion is motion in a straight line.
  • Similarly, circular motion is motion in a circle.
  • At any instant in time, the particle is moving in a particular straight-line direction with that speed.
  • Constant angular velocity in a circle is known as uniform circular motion.
  • A vector diagram illustrating circular motion.

• Constant Velocity

  • Motion with constant velocity is one of the simplest forms of motion.
  • Constant direction constrains the object to motion to a straight path.
  • Therefore the motion of an object at constant velocity is represented by a straight line: $x=x_0+vt$, where $x_0$ is the displacement when $t=0$ (or at the y-axis intercept).
  • In graphical terms, the velocity can be interpreted as the slope of the line.
  • When an object is moving with constant velocity, it does not change direction nor speed and therefore is represented as a straight line when graphed as distance over time.

• Key Points: Range, Symmetry, Maximum Height

  • Projectile motion is a form of motion where an object moves in parabolic path.
  • Projectile motion is a form of motion where an object moves in a bilaterally symmetrical, parabolic path.
  • If you were to draw a straight vertical line from the maximum height of the trajectory, it would mirror itself along this line.
  • This is also the point where you would draw a vertical line of symmetry.
  • There is no acceleration in this direction since gravity only acts vertically. shows the line of range.

• 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.
  • This angle is the angle between a straight line drawn from the center of the circle to the objects starting position on the edge and a straight line drawn from the objects ending position on the edge to center of the circle.
  • There is an easy way to produce simple harmonic motion by using uniform circular motion.
  • Describe relationship between the simple harmonic motion and uniform circular motion

• Components of a Vector

  • Vectors are geometric representations of magnitude and direction which are often represented by straight arrows, starting at one point on a coordinate axis and ending at a different point.
  • Next, draw a straight line from the origin along the x-axis until the line is even with the tip of the original vector.
  • To find the vertical component, draw a line straight up from the end of the horizontal vector until you reach the tip of the original vector.
  • Whenever you see motion at an angle, you should think of it as moving horizontally and vertically at the same time.
  • Simplifying vectors in this way can speed calculations and help to keep track of the motion of objects.

• The First Law: Inertia

  • Newton’s first law of motion describes inertia.
  • According to this law, a body at rest tends to stay at rest, and a body in motion tends to stay in motion, unless acted on by a net external force.
  • The object is either at rest and the velocity is zero or it moves in a straight line with a constant speed.
  • This is called uniform motion.
  • Newton says that a body in motion will stay in motion until an outside force acts upon it.

• The Third Law: Symmetry in Forces

  • The third law of motion states that for every action, there is an equal and opposite reaction.
  • Newton used these laws to explain and explore the motion of physical objects and systems.
  • The object is either at rest and the velocity is zero or it moves in a straight line with a constant speed.
  • You have undoubtedly witnessed this law of motion.
  • When a swimmer pushes off the wall, the swimmer is using the third law of motion.

• Newton and His Laws

  • Newton's laws of motion describe the relationship between the forces acting on a body and its motion due to those forces.
  • The laws of motion will tell you how quickly the car will move from your pushing.
  • There are three laws of motion:
  • First law: If an object experiences no net force, then its velocity is constant: the object is either at rest (if its velocity is zero), or it moves in a straight line with constant speed (if its velocity is nonzero).
  • Apply three Newton's laws of motion to relate forces, mass, and acceleration