Kinematics of Machines: Overview, Questions, Preparation

Kinematics is the study of motion, without regard to forces or torque. It is the first step in the analysis or design of a mechanism. To describe motion, kinematics studies the trajectories of points, lines and other geometric objects including their differential properties (such as velocity, displacement, time and acceleration). 

The motion of the rigid body is a combination of translation and rotation. If a body is fixed at a point along the line, it has only rotational motion. The rotational about a fixed axis involves only one independent variable to describe the motion.

Reference: NCERT

Angular displacement is a vector quantity measured in radians and defined as the shortest angle between the initial and final points of an object undergoing circular motion about a fixed point.

θ = s/r

Angular velocity is the time rate of change of angular displacement. 

ω = dθ/dt

Angular acceleration α is defined as the time rate of change of angular velocity.

α = dω /dt

The kinematical quantities in rotational motion, angular displacement (θ), angular velocity (ω) and angular acceleration (α) respectively correspond to kinematic quantities in linear motion, displacement (x), velocity (v) and acceleration (a).

Reference: NCERT

Where θ൦ = initial angular displacement of the rotating body and ω൦ = initial angular velocity of the body.

Formulas of Kinematics

Kinematics is a vast subject in physics. At this level, one must know the definitions and formulas of kinematics. The problem-based questions are more from this topic. The topic has a weightage of 5 marks.

 v=v0+at

v0 = 0,  (it started at rest) ; t= 1.5 sec; a = -9.81 m/s^2(freely falling object).

v=v0+at = 0 +(- 9.81)*1.5 = -14.71 m/s.

2. A car starts from rest and accelerates uniformly over a time 4.78 seconds for a distance of 110 m. Find out the acceleration of the Car?

GivenΔx = 110m; t= 4.78s; v = 0 (rest)  

 Δx = v0t+1/2at2

110 = 0*4.78+1/2 *a*(4.78)^2

110 =11.4242a

a=9.62 m/s^2

3. A kangaroo is capable of jumping to a height of 1.62 m. Determine the takeoff speed of the kangaroo?

 v2=v02+2aΔx

v2= 0; a =-9.81 m/S^2 ; Δx = 1.62 m

0 = v0^2 +2*(-9.81)*1.62

v0^2= 31.87

v0 =5.64 m/s

1. What is the difference between kinematics, kinetics and dynamics?

2. How is kinematics used in real life?

3. When can kinematics not be used?

4. What are scalars and vectors?

5. What are the different types of Machines?