This chapter explores the motion of objects in a plane, focusing on vectors, velocity, acceleration, projectile motion, and uniform circular motion.
MOTION IN A PLANE – Formula & Equation Sheet
Essential formulas and equations from Physics Part - I, tailored for Class 11 in Physics.
This one-pager compiles key formulas and equations from the MOTION IN A PLANE chapter of Physics Part - I. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
r = xi + yj
r is the position vector, xi and yj are the components along the x and y axes respectively. This equation defines the position of an object in a 2D plane.
v = dr/dt
v is the velocity vector, dr is the displacement vector, and dt is the time interval. It defines the relationship between displacement and time.
a = dv/dt
a is the acceleration vector, dv is the change in velocity, and dt is the time interval. This equation relates acceleration with the change in velocity over time.
v = v0 + at
v is the final velocity, v0 is the initial velocity, a is the constant acceleration, and t is time. This formula is used for linear motion with uniform acceleration.
s = v0t + (1/2)at²
s is the displacement, v0 is the initial velocity, a is acceleration, and t is time. This relation gives the displacement of an object under constant acceleration.
R = (v0² sin(2θ))/g
R is the range of the projectile, v0 is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity. This formula calculates the horizontal range of a projectile.
h = (v0² sin²(θ))/(2g)
h is the maximum height reached by the projectile, v0 is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity. This formula gives the peak height of a projectile's trajectory.
T = (2v0 sin(θ))/g
T is the time of flight, v0 is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity. This formula calculates the total time a projectile is in the air.
v_x = v_0 cos(θ)
v_x is the horizontal component of the initial velocity, v_0 is the initial velocity, and θ is the angle of projection. This gives the horizontal velocity component of a projectile.
v_y = v_0 sin(θ) - gt
v_y is the vertical component of the velocity at time t, v_0 is the initial vertical velocity, g is the acceleration due to gravity, and t is time. This relation describes the vertical motion of a projectile.
Equations
A + B = R
This equation expresses the vector addition of two vectors A and B to yield a resultant vector R, illustrating the concept of vector addition.
|R| = √(Ax² + Ay²)
This formula calculates the magnitude of the resultant vector R from its components Ax and Ay. Useful for determining the total effect of multiple displacements.
A = λa + μb
This equation represents the resolution of a vector A into two component vectors a and b, where λ and μ are scalars. This helps in analyzing complex vectors.
s = (1/2)(u + v)t
s is the total distance or displacement, u is the initial velocity, v is the final velocity, and t is the time. This formula is often used to calculate displacement during uniformly accelerated motion.
R = v²/g
R denotes the range of a projectile when projected vertically or horizontally at maximum height in vacuum. Derived from equations governing projectile motion.
a_c = v²/R
a_c is the centripetal acceleration, v is the velocity of the object, and R is the radius of the circular path. This equation describes the acceleration experienced by an object moving in a circle.
θ = tan⁻¹(v_y/v_x)
This expression gives the angle of the resultant velocity vector θ in terms of its components v_y (vertical) and v_x (horizontal). Used for determining direction in projectile motion.
v = ωR
This formula relates linear velocity v of an object in circular motion to its angular velocity ω and the radius R of the circular path. It shows how rotational movement translates to linear motion.
t = 2R/v
This equation gives the time taken for an object to travel a circular path of circumference 2πR at a constant speed v. Useful for computing time in circular motion.
v_{avg} = (s/t)
This represents the average velocity, where s is the displacement and t is the time taken. It provides a fundamental concept for understanding motion.
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