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Kinematics and Dynamics of Particles and Rigid Bodies in Plane Motion Study Notes for GATE ME Exam
By BYJU'S Exam Prep
Updated on: September 25th, 2023
Kinematics and Dynamics of Particles and Rigid Bodies in Plane Motion Study Notes for GATE ME Exam: In this article, know the important pointers for Kinematics and Dynamics of Particles and Rigid Bodies in Plane Motion like types and other terminologies, which can help you to score well in GATE ME, ISRO, and other competitive exams.
Kinematics focuses on the description and analysis of motion without considering the forces that cause it. By studying concepts such as displacement, velocity, acceleration, and time, we gain a comprehensive understanding of how objects move through space and time. Whether it’s the graceful flight of a bird, the swift trajectory of a race car, or the simple pendulum swinging back and forth, kinematics provides us with the tools to precisely describe their motions. Let’s discuss more about the Kinematics and Dynamics of Particles and Rigid Bodies in Plane Motion with this article.
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Table of content
What is Plane Motion?
A rigid body is said to perform plane motion when all parts of the body move in parallel planes.
- If every line in the body remains parallel to its original position at all times, the body is said to be in translation motion.
- All the particles forming a rigid body move along parallel paths in translation motion.
- A curvilinear translation motion takes place when all particles which form a rigid body do not move along parallel straight lines but move along a curved path.
What is Straight Line Motion?
In a straight-line motion, acceleration is constant both in magnitude and direction. Three equations that we usually apply in a straight-line motion are:
v=u+at
s=ut+½ at2
v2=u2+2as
u is initial velocity, v is final velocity, a is acceleration of the body, t is time, and s is the distance traveled by the body.
Distance traveled in the nth second:
sn=u+½ a(2n-1)
Angular Acceleration and Angular Velocity
Consider a rod pivoted at a point and rotating about it.
Angular velocity (ω=dθ/dt; ie. change in angular displacement per unit time)
Angular acceleration α=dω/dt ⇒ α=d2θ/dt2
Where θ = angle between displacement.
In rotatory motion, the equations that were used in the straight-line motion change slightly to the following:
θ=ωt
α=0
ω=ω0+αt
θ=ω0t+½ αt2
ω2=ω02+2αθ
ω0 being the initial angular velocity, ω being the final angular velocity, α being the angular acceleration, and θ being angular displacement.
Angular displacement in the nth second: θn=ω0+½ α(2n-1)
Centre of Mass of Continuous Body
For a continuous body, the center of mass can be defined:
- For a uniform rectangular, square, or circular plate, the COM lies at its center.
- COM of semicircular ring
- CM of semicircular disc
- CM of a hemispherical shell
- CM of a solid hemisphere
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Law of Conservation of Linear Momentum
Linear momentum (p) can be defined as the product of mass and velocity.
Where
- K = kinetic energy of the particle
- F = net external force applied to the body
- P = momentum
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