What is Kinematics of particles: Definition and 13 Discussions
Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. The study of how forces act on bodies falls within kinetics, not kinematics. For further details, see analytical dynamics.
Kinematics is used in astrophysics to describe the motion of celestial bodies and collections of such bodies. In mechanical engineering, robotics, and biomechanics kinematics is used to describe the motion of systems composed of joined parts (multi-link systems) such as an engine, a robotic arm or the human skeleton.
Geometric transformations, also called rigid transformations, are used to describe the movement of components in a mechanical system, simplifying the derivation of the equations of motion. They are also central to dynamic analysis.
Kinematic analysis is the process of measuring the kinematic quantities used to describe motion. In engineering, for instance, kinematic analysis may be used to find the range of movement for a given mechanism and working in reverse, using kinematic synthesis to design a mechanism for a desired range of motion. In addition, kinematics applies algebraic geometry to the study of the mechanical advantage of a mechanical system or mechanism.
Homework Statement
Homework Equations
$$h=ut+1/2at^2$$ $$h=x\tan\theta-1/2g\frac{x^2}{u^2\cos^2\theta}$$
The Attempt at a Solution
I tried to take a random angle theta for the lower particee and then using the equation of the upper particle tried to solve them together and find condition for...
Homework Statement
11.10 The acceleration of a particle is directly proposional to the time t.
At t = 0, the velocity of the particle is v = 16 in./s. Knowing that v = 15 in./s
and that x = 20 in. when t = 1 s, determine the velocity, the position, and
the total distance traveled when t = 7s...
Homework Statement
11.8 The motion of a particle is defined by the relation ##x=t^3 - 6t^2 - 36t - 40,
where x and t are expressed in feet and seconds, respectively. Determine
(a) when the velocity is zero, (b) the velocity, the acceleration, and the total
distance traveled when x = 0...
Homework Statement
11.7 The motion of a particle is defined by the relation ##x = 2t^3 - 15t^2 + 24t + 4
where x is expressedin meters and t in seconds. Determine (a) when the velocity zero ,
(b) the position and the total distance traveled when the acceleration is zero
Homework EquationsThe...
Homework Statement
The motion of a particle is defined by the relation ##x = 6t^4 - 2t^3 - 12t^2 + 3t + 3##, where
x and t are expressed in meters and seconds, respectively. Detrmine the time, the position,
and the velocity when a = 0.
Homework EquationsThe Attempt at a Solution
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Can...
Homework Statement
A loaded railroad car is rolling at a constant velocity when it couples with a spring and dashpot
bumber system. After the coupling, the motion of the car is defined by the relation
##x = 60e^{-4.8t} sin16t##, where x and t are expressed in millimeters and seconds...
Homework Statement
Refer to figure please.
Homework Equations
∑Fy=0 before string is cut
The Attempt at a Solution
I tried summing the two forces in the y direction before the strings were cut which would be the two tensions at a sin40° and minus the weight of the ball(mg). That gave me T in...
Hi guys. I'm new here. If i did any mistake please forgive me.
First of all I have a simple problem need all of you to help me.
Here is the problem
The acceleration of a particle is defined by the relation a = -k√v, where k is constant.
Knowing that
x = 0 and v =...
Homework Statement
A particle moves in a plane. The particle (x,y) position on the plane is given by:
x = -34t^4 − 28t^3 + 7
y = 25t^2 + 13t^3 + 5
Therefore the particle's displacement [from the (x,y) origin) at time t = 68 s is
(736000000m) i + (4200000m)j
(a) What is the...
Homework Statement
The slotted arm OA forces the small pin to move in the fixed spiral guide defined by r=Kθ. Arm OA starts from rest at θ=π/4 and has a constant counterclockwise angular acceleration \ddot{theta} =α. Determine the magnitude of the acceleration of the pin when θ=3π/4...
Homework Statement
http://img402.imageshack.us/img402/5733/problemvm7.th.jpg
I had to draw in that line. It was suppose to show a dotted line of the projectile, but the page did not scan well.
Homework Equations
The Attempt at a Solution
First atempt...
it is known from t=2 to t=10 the accelareation of a particle is inversely proportional to the cube of time t.when t=2, v=-15 and when t=10 ,v=0.36.knowing that the particle is twice as far from the origin when t=2 and t=10,determine the position of the particle when t=2 and t=10
the answer...
the motion of a particle is defined by x=2(t^3) - 18(t^2) + 48t - 16 where x=meter and t=sec.determine the total distance traveled when the acceleration is zero.
the answer is 44m.
pls help...thanx...