Kinematics Equations – What is Kinematics | Inverse Kinematics

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

These equations link five kinematic variables:

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

Essentially, kinematics equations can derive one or more of these variables if the others are given. These equations define motion at either constant velocity or at constant acceleration. Because kinematics equations are only applicable at a constant acceleration or a constant speed, we cannot use them if either of the two is changing.

Inverse Kinematics:

Inverse Kinematics does the reverse of kinematics and in case we have the endpoint of a particular structure, certain angle values would be needed by the joints to achieve that endpoint. It is a little difficult and has generally more than one or even infinite solutions.

There are four basic kinematics equations:

  1. \(\begin{array}{l}v=v_{0}+at\end{array} \)  
  2. \(\begin{array}{l}\Delta x=(\frac{v+v_{0}}{2})t\end{array} \)  
  3. \(\begin{array}{l}\Delta x= v_{0}t+\frac{1}{2}at^{2}\end{array} \)  
  4. \(\begin{array}{l}v^{^{2}}=v_{o}^{2}+2a\Delta x\end{array} \)  

It can be noticed that if any four of the variables are given, we can easily calculate the fifth variable using kinematic equations.

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

For example, if it is given that a car is travelling and it accelerates from its resting position with an acceleration of 6.5 m/s2 for a time span of 8 seconds, reaching a final velocity of 42 m/s, east and a displacement of 120 m, then the motion of this car is fully described. Now, if anyone of this information was not provided, we could have easily calculated it with the help of kinematics equations.

Rotational Kinematics Equations

Till now, we were looking at the Translational or linear kinematics equation which deals with the motion of a linearly moving body. There is another branch of kinematics equations which deals with the rotational motion of anybody. These are, however, just a corollary of the previous equations with just the variables changed.

  • Displacement is replaced by a change in angle.
  • Initial and final velocities are replaced by initial and final angular velocity.
  • Acceleration is replaced by angular acceleration
  • Time is the only constant.

Frequently Asked Questions – FAQs

Q1

What is centripetal acceleration?

When an object is moving in a circle and its acceleration vector is pointed towards the centre of that circle, it is known as centripetal acceleration. The unit of centripetal acceleration is m/s2.

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Q2

What is kinematics?

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

Q3

What is radial acceleration?.

When there is an acceleration of an object along the radius directed towards the centre, it is known as radial acceleration. It is expressed as radian/sec2.

Q4

Define kinetic energy.

The kinetic energy is the measure of the work an object can do by virtue of its motion.

Q5

When is the kinetic energy maximum?

The kinetic energy is maximum when the potential energy is minimum, and this occurs when the velocity is maximum and the mass is at the equilibrium position.

Compare Equations of Motion for Rotational Motion and Linear Motion

Rotational Motion (α = constant)Linear Motion (a = constant)
\(\begin{array}{l}\omega =\omega_{0}+\alpha t\end{array} \)  \(\begin{array}{l}v=v_{0}+at\end{array} \)  
\(\begin{array}{l}\Theta =\frac{1}{2}(\omega+\omega_{0})t\end{array} \)  \(\begin{array}{l}x=\frac{1}{2}(v_{0}+v)t\end{array} \)  
\(\begin{array}{l}\Theta =\omega_{0}t+\frac{1}{2}\alpha t^{2}\end{array} \)  \(\begin{array}{l}x=v_{0}t+\frac{1}{2}at^{2}\end{array} \)  
\(\begin{array}{l}\omega^{2} =\omega_{0}^{2}+2\alpha \Theta\end{array} \)  \(\begin{array}{l}v^{2}=v_{0}^{2}+2ax\end{array} \)  

Er. Neeraj K.Anand is a freelance mentor and writer who specializes in Engineering & Science subjects. Neeraj Anand received a B.Tech degree in Electronics and Communication Engineering from N.I.T Warangal & M.Tech Post Graduation from IETE, New Delhi. He has over 30 years of teaching experience and serves as the Head of Department of ANAND CLASSES. He concentrated all his energy and experiences in academics and subsequently grew up as one of the best mentors in the country for students aspiring for success in competitive examinations. In parallel, he started a Technical Publication "ANAND TECHNICAL PUBLISHERS" in 2002 and Educational Newspaper "NATIONAL EDUCATION NEWS" in 2014 at Jalandhar. Now he is a Director of leading publication "ANAND TECHNICAL PUBLISHERS", "ANAND CLASSES" and "NATIONAL EDUCATION NEWS". He has published more than hundred books in the field of Physics, Mathematics, Computers and Information Technology. Besides this he has written many books to help students prepare for IIT-JEE and AIPMT entrance exams. He is an executive member of the IEEE (Institute of Electrical & Electronics Engineers. USA) and honorary member of many Indian scientific societies such as Institution of Electronics & Telecommunication Engineers, Aeronautical Society of India, Bioinformatics Institute of India, Institution of Engineers. He has got award from American Biographical Institute Board of International Research in the year 2005.