Kinematics Equations

Kinematics equation

Kinematics, a branch of physics that defines motion to space with time, ignoring the cause of that motion, this is called kinematics. The Kinematics equation is a set of equations that can derive an unknown aspect of a body’s motion if the other aspects are provided.

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There are four basic kinematics equations:

v = v 0 + a t, Δ x = ( v + v 0 2 ) t, Δ x = v 0 t + 1 2 a t 2, v 2 = v o 2 + 2 a Δ x.

These Mathematical Expressions Link 5 Kinematic Variables:

  • Initial Velocity v0
  • Final Velocity denoted by v
  • Time interval (denoted by t)
  • Displacement (denoted by Δx)
  • Constant acceleration (denoted by a)

The kinematics equations can derive one or more of these variables if the others are given. All these equations define the motions at either constant velocity or at constant acceleration. Because the kinematics equations are only applicable when a constant acceleration or a constant speed, we cannot use them if they change.

Inverse Kinematics

Inverse Kinematics is a mathematical technique that is used to solve the opposite problem of regular kinematics. Also, Inverse kinematics reverses kinematics, thus if we know the endpoint of a structure, the joints must have a certain value of angle to reach the endpoint. It’s a little challenging, and there are typically multiple or infinite solutions.

Four Basic Equations of Inverse Kinematics:

  1. v = v₀ + at
  2. Δx = (v + v₀)/2 * t
  3. Δx = v₀t + 1/2at²
  4. v² = v₀² + 2aΔx

NOTE: If any four of the variables are given, we can easily find the fifth variable using kinematic equations.

Inverse Kinematics
Inverse Kinematics

Rotational Kinematics Equations

Rotational kinematics equations are the counterparts of linear kinematics equations. we were looking at the Translational or linear kinematics equation which deals with the motion of a linearly moving body. Another area of kinematics equations addresses an individual’s rotational motion. But these are just the previous equations’ corollaries with the variables switched.

Four Basic Rotational Kinematics Equations, Analogous to the Four Basic Linear Equations:

  1. θ = ω₀t + 1/2αt²
  2. ω = ω₀ + αt
  3. θ = (ω + ω₀)/2 * t
  4. ω² = ω₀² + 2αθ

Rotational Motion (α = constant) VS Linear Motion (a = constant)

Rotational Motion (α = constant)Linear Motion (a = constant)
ω = ω₀ + αtv = v₀ + at
θ = (ω + ω₀)/2 * tx = (v + v₀)/2 * t
θ = ω₀t + 1/2αt²θ = ω₀t + 1/2αt²
ω² = ω₀² + 2αθω² = ω₀² + 2αθ

Frequently Asked Questions Related Kinematics Equations

What is kinematics?

Kinematics is a of physics that considers the motion with respect to time and space, ignoring the cause of that motion is called kinematics. The Kinematics equations are a set of equations that can derive an unknown aspect of a body’s motion if the other aspects are provided.

What is kinetic energy?

Kinetic energy is a way to measure how much work something can do just by it’s motion.

What is Radial Acceleration?.

When an object moves faster along its radius and toward its center, this is called radial acceleration. Radian/sec2 is the way to write it.

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