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.
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:
u is initial velocity, v being final velocity, a being acceleration of the body, t being time, and s being distance travelled by the body.
Distance travelled in the nth second:
Projectile Motion
Type of motion where velocity has two components, one in the vertical direction and another one in the horizontal direction. Component of velocity in the horizontal direction is constant during the flight of the body as no acceleration in the horizontal direction is present. Consider the following projectile motion:
Maximum height
Time of flight
Range
u is the initial velocity.
- The vertical component of velocity becomes zero at the maximum height.
- A particle located on the axis of rotation has zero velocity and zero acceleration (in case a rigid body moves in a circular path).
- The air resistance is considered negligible during projectile motion.
Angular acceleration and Angular Velocity
Consider a rod pivoted at a point and rotating about it.
Angular velocity (change in angular displacement per unit time)
Angular acceleration
Where θ = angle between displacement.
In rotatory motion, the equations that were used in the straight-line motion, changes slightly to the following:
ω0 being initial angular velocity, ω being final angular velocity, α being the angular acceleration, and θ being angular displacement.
Angular displacement in the nth second:
Relation between Linear and Angular Quantities
The relationships between linear and angular quantities in rotational motion are listed below:
et and er are tangential and radial unit vectors.
Linear velocity
Linear acceleration (Net)
Tangential acceleration (rate of change of speed)
Centripetal acceleration
Net acceleration,
Where ar = centripetal acceleration
at = tangential acceleration
Centre of Mass of Continuous Body: For a continuous body, centre of mass can be defined as
- Centre of mass about
- Centre of mass about
- Centre of mass about
- For a uniform rectangular, square or circular plate, the CM lies at its centre.
- CM of semicircular ring
- CM of semicircular disc
- CM of a hemispherical shell
- CM of a solid hemisphere
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
Rocket Propulsion- Consider a rocket of mass m0 at time t = 0, at any time t, v is its velocity and m is the mass at that moment. Initially, let the velocity of the rocket be u.
- Thrust force on the rocket
Where, rate at which mass is ejecting,
vr is the relative velocity of ejecting mass (exhaust velocity)
- Weight of the rocket w = mg
- The net force on the rocket
- Net acceleration of the rocket
m0 is the mass of the rocket at time t = 0
m is the mass of rocket at time t
Important Tips for GATE Preparation
- How to use Virtual Calculator for GATE 2022
- Topper's strategy for GATE Exam preparation
- GATE 2022 Exam Syllabus
Accelerate your GATE 2022 preparations with BYJU's Exam Prep Online Classroom Program
Related Important Links
Thanks
Dream Strive Succeed
Comments
write a commentMysura ReddyDec 3, 2017
Subash SahuDec 9, 2017
jithin mohanMar 31, 2018
ANITA RANI PARIDAOct 8, 2018
Manu SNov 13, 2018
Surya SuriyaJun 18, 2019
Kapil VermaSep 12, 2019
Test series material full solved online test series in the PDF format available for 2019
Interested aspirant contact me at whatsapp 8225950652 #GATE2020
#ese2020
Shivam AgrawalJul 30, 2020
Pls relpy 🙏
Manisha ShettyAug 21, 2020
Krishna KanthSep 14, 2020