acceleration

Examples of acceleration in the following topics:

• Angular Acceleration, Alpha

  • Angular acceleration is the rate of change of angular velocity.
  • In equation form, angular acceleration is expressed as follows:
  • The units of angular acceleration are (rad/s)/s, or rad/s2.
  • This acceleration is called tangential acceleration, at.
  • This acceleration is called tangential acceleration.

• Centripetial Acceleration

  • Since the speed is constant, one would not usually think that the object is accelerating.
  • Thus, it is said to be accelerating.
  • One can feel this acceleration when one is on a roller coaster.
  • This feeling is an acceleration.
  • A brief overview of centripetal acceleration for high school physics students.

• Motion with Constant Acceleration

  • Constant acceleration occurs when an object's velocity changes by an equal amount in every equal time period.
  • Acceleration can be derived easily from basic kinematic principles.
  • Assuming acceleration to be constant does not seriously limit the situations we can study and does not degrade the accuracy of our treatment, because in a great number of situations, acceleration is constant.
  • When it is not, we can either consider it in separate parts of constant acceleration or use an average acceleration over a period of time.
  • Due to the algebraic properties of constant acceleration, there are kinematic equations that relate displacement, initial velocity, final velocity, acceleration, and time.

• Particle Accelerator

  • While current particle accelerators are focused on smashing subatomic particles together, early particle accelerators would smash entire atoms together, inducing nuclear fusion and thus nuclear transmutation.
  • There are two basic classes of accelerators: electrostatic and oscillating field accelerators.
  • Electrostatic accelerators use static electric fields to accelerate particles.
  • Despite the fact that most accelerators (with the exception of ion facilities) actually propel subatomic particles, the term persists in popular usage when referring to particle accelerators in general.
  • The main accelerator is the ring above; the one below (about half the diameter, despite appearances) is for preliminary acceleration, beam cooling and storage, etc.

• Relationship Between Torque and Angular Acceleration

  • Torque is equal to the moment of inertia times the angular acceleration.
  • Torque and angular acceleration are related by the following formula where is the objects moment of inertia and $\alpha$ is the angular acceleration .
  • If you replace torque with force and rotational inertia with mass and angular acceleration with linear acceleration, you get Newton's Second Law back out.
  • Torque, Angular Acceleration, and the Role of the Church in the French Revolution
  • Express the relationship between the torque and the angular acceleration in a form of equation

• Constant Angular Acceleration

  • Constant angular acceleration describes the relationships among angular velocity, angle of rotation, and time.
  • We have already studied kinematic equations governing linear motion under constant acceleration:
  • Similarly, the kinematics of rotational motion describes the relationships among rotation angle, angular velocity, angular acceleration, and time.
  • By using the relationships a=rα, v=rω, and x=rθ, we derive all the other kinematic equations for rotational motion under constant acceleration:
  • Relate angle of rotation, angular velocity, and angular acceleration to their equivalents in linear kinematics

• Graphical Interpretation

  • Acceleration is accompanied by a force, as described by Newton's Second Law; the force, as a vector, is the product of the mass of the object being accelerated and the acceleration (vector), or $F=ma$.
  • Because acceleration is velocity in $\displaystyle \frac{m}{s}$ divided by time in s, we can further derive a graph of acceleration from a graph of an object's speed or position.
  • From this graph, we can further derive an acceleration vs time graph.
  • The acceleration graph shows that the object was increasing at a positive constant acceleration during this time.
  • This is depicted as a negative value on the acceleration graph.

• Overview of Non-Uniform Circular Motion

  • The change in direction is accounted by radial acceleration (centripetal acceleration), which is given by following relation: $a_r = \frac{v^2}{r}$.
  • The change in speed has implications for radial (centripetal) acceleration.
  • A change in $v$ will change the magnitude of radial acceleration.
  • The greater the speed, the greater the radial acceleration.
  • The corresponding acceleration is called tangential acceleration.

• Kinematics of UCM

  • The acceleration can be written as:
  • This acceleration, responsible for the uniform circular motion, is called centripetal acceleration.
  • Any force or combination of forces can cause a centripetal or radial acceleration.
  • According to Newton's second law of motion, net force is mass times acceleration.
  • For uniform circular motion, the acceleration is the centripetal acceleration: $a = a_c$.

• Rotational Inertia

  • The first example implies that the farther the force is applied from the pivot, the greater the angular acceleration; another implication is that angular acceleration is inversely proportional to mass.
  • The greater the force, the greater the angular acceleration produced.
  • The more massive the wheel, the smaller the angular acceleration.
  • If you push on a spoke closer to the axle, the angular acceleration will be smaller.
  • Explain the relationship between the force, mass, radius, and angular acceleration