**Plane Motion:** When all parts of the body move in a parallel plane then a rigid body said to perform plane motion.

- The motion of rigid body is said to be translation, if every line in the body remains parallel to its original position at all times.
- In translation motion, all the particles forming a rigid body move along parallel paths.
- If all particles forming a rigid body move along parallel straight line, it is known as rectilinear translation.
- If all particles forming a rigid body does not move along a parallel straight line but they move along a curve path, then it is known as curvilinear translation.

**Straight Line Motion:** It defines the three equations with the relationship between velocity, acceleration, time and distance travelled by the body. In straight line motion, acceleration is constant.

Where, *u* = initial velocity, *v* = final velocity, *a* = acceleration of body, *t* = time, and *s* = distance travelled by body.

Distance travelled in *n*th second:

**Projectile Motion:** Projectile motion defines that motion in which velocity has two components, one in horizontal direction and other one in vertical direction. Horizontal component of velocity is constant during the flight of the body as no acceleration in horizontal direction.

Let the block of mass is projected at angle θ from horizontal direction.

Maximum height

Time of flight

Range

Where, *u* = initial velocity.

- At maximum height vertical component of velocity becomes zero.
- When a rigid body move in circular path centred on the same fixed axis, then the particle located on axis of rotation have zero velocity and zero acceleration.
- Projectile motion describes the motion of a body, when the air resistance is negligible.

**Rotational Motion with Uniform Acceleration:** Uniform acceleration occurs when the speed of an object changes at a constant rate. The acceleration is the same over time. So, the rotation motion with uniform acceleration can be defined as the motion of a body with the same acceleration over time.

Let the rod of block rotation about a point in horizontal plane with angular velocity.

Angular velocity (change in angular displacement per unit time)

Angular acceleration

Where θ = angle between displacement.

In case of angular velocity, the various equations with the relationships between velocity, displacement and acceleration are as follows.

Where ω_{0} = initial angular velocity, ω = final angular velocity, α = angular acceleration, and θ = angular displacement.

Angular displacement in *n*th second:

**Relation between Linear and Angular Quantities **

There are following relations between linear and angular quantities in rotational motion.

*e _{r}* and

*e*are radial and tangential unit vector.

_{t}Linear velocity

Linear acceleration (Net)

Tangential acceleration (rate of change of speed)

Centripetal acceleration

Net acceleration,

Where *a _{r}* = centripetal acceleration

*a _{t}* = tangential acceleration

**Centre of Mass of Continuous Body:** Centre of mass of continuous body can be defined as

- Centre of mass about
- Centre of mass about
- Centre of mass about
- CM of uniform rectangular, square or circular plate lies at its centre.
- CM of semicircular ring

- CM of semicircular disc

- CM of hemispherical shel

- CM of solid hemisphere

**Law of Conservation of Linear Momentum**

The product of mass and velocity of a particle is defined as its linear momentum (*p*).

Where, *K* = kinetic energy of the particle

*F* = net external force applied to body

*P* = momentum

**Rocket Propulsion**

Let *m*_{0} be the mass of the rocket at time *t* = 0, *m* its mass at any time *t* and v its velocity at that moment. Initially, let us suppose that the velocity of the rocket is *u*.

- Thrust force on the rocket

Where, rate at which mass is ejecting

*v _{r}* = relative velocity of ejecting mass (exhaust velocity)

- Weight of the rocket w = mg
- Net force on the rocket
- Net acceleration of the rocket

Where, *m*_{0} = mass of rocket at time *t* = 0

*m* = mass of rocket at time

You can avail of Online Classroom Program for all AE & JE Exams:

**Online Classroom Program for AE & JE Exams (12+ Structured LIVE Courses and 160+ Mock Tests)**

You can avail of BYJU'S Exam Prep Test Series specially designed for all AE & JE Exams:

**BYJU'S Exam Prep Test Series AE & JE (160+ Mock Tests)**** **

Thanks,

Team BYJU'S Exam Prep

*Download **BYJU'S Exam Prep APP** , for best **Exam Preparation , Free Mock Test, Live Classes*

## Comments

write a comment