Kinematics Flashcards
Chapter 3
Kinematics
The branch of physics that deals with objects in motion without considering the forces that cause the motion
Motion
When a body does not change its position with time, we can say that the body is at rest, while if a body changes its position with time
Translational (Linear) Motion
A type of motion in which all parts of an object move the same distance in a given time
-Rectilinear motion refers to motion along a straight line.
Ex: An object thrown in the air follows a parabolic trajectory.
-Curvilinear motion refers to motion along a curved path. can be circular, parabolic, or any other type of curve. Ex: A person walking in a straight line.
Rotational Motion
When an object moves about an axis and different parts of it move by different distances in a given interval of time
Ex: A spinning top, a rotating wheel, or the Earth spinning about its own axis.
Circular Motion
Motion that refers specifically to the motion of an object along a circular path.
-Can be uniform (constant speed) or non-uniform (changing speed).
-In circular motion, the object is moving around a fixed point
-Typically analyzed in terms of its tangential speed and centripetal acceleration.
Ex: A car moving along a curved road, or a planet orbiting the sun.
Oscillatory (Vibratory) Motion
A specific periodic motion that involves the to and fro movement of a body
Directions/Dimensions
-One Dimensional Motion is the motion of a particle moving along a straight line
-Two-dimensional Motion is a particle moving along a curved path in a plane
-Three-dimensional motion describes particles moving randomly in space
Sate of Motion
-Uniform Motion: When a body travels equal distances in equal intervals of time
-Non-uniform Motion: When a body travels unequal distances in equal time intervals
Displacement
The distance moved by a body in a specific direction
-d =df−di
-df: Final position
-di: Initial position
-d: Displacement
-d = (dx,dy)(for2Dmotion)
_________
-2D Magnitude ∣d∣ = /dx²+dy²
-d =( dx,dy,dz)(for3Dmotion)
______________
-3D Magnitude ∣d ∣= /dx² +dy²+dz²
-d(t)=∫∫a(t)dt
Velocity
The rate of change of displacement in a given direction
v = Δx = xf -xi = displacement
Δt tf - ti change in time
-v(t) = dx
d(t)
-v(t)=∫a(t)dt
Instantaneous Velocity
v = Δx
Δt
Average Velocity
a = Δx = vf -vi
Δt = tf - ti
Acceleration
The rate of change of velocity
a = change in velocity = (v - u)/2
time
a = dx = d2x
d(t) d2(t)
1st Equation of Motion
(1)a = v - u
t
(2)v = u + at
2nd Equation of Motion
(1) s = (v + u)t -v = u + at
( t )
s = (u + at + u)t
2
s = (2u + at)t
2
s = ut + 1/2at²
Third Equation of Motion
s = 1/2(u+v)t
a = (v-u), t = (v-u), s = (v+u)t
t a 2
s = (u+v )*(v-u)
2 a
s = (v² - u²), cross multiply
2a
2as = v² - u²
v² = u² + 2as
Rotational Kinematics Formulas (4)
(1.)w = wi + at
(2).θ = θi +(1/2)(wi + w)t
(3).θ = θi + (wi)t + (at²)/2
(4).w² = wi² +2a(θ - θi)
Equations of Motion Under Gravity (3)
When working with gravity
-(1). v = u + gt
-(2). H = ut + 1/2gt²
-(3). v² = u² + 2gH
When working against gravity
-(1). v = u - gt
-(2). H = ut - 1/2gt²
-(3). v² = u² - 2gH
Projectile
A projectile is anything that is given an initial velocity and left to move on its own in the presence of a constant force field
Properties of projectiles
Projectiles have both vertical and horizontal component which are independent of each other
-Acceleration due to gravity for the vertical component is g while that of the horizontal component is zero
Free Falling Body
An object that moves under the influence of gravity only
Vertical Component of Velocity
vy = uy ± gt,
uy = ysin(θ)
Horizontal Component of Velocity
vx = ux +axt, ax = 0
ux = ucos(θ)
Angle of Projection (θ)
The angle between the projection and the horizontal
tanθ = vy = usinθ - gt
vx ucosθ
θ = tan⁻¹(vy) = (usinθ - gt)
(vx) ( ucosθ )
Trajectory
The path followed by the projectile
x = (ucosθ)t, —> t = x
ucosθ
y = uyt - 1/2gt² , uy = uSinθ,
y = usinθ(t) -1/2gt²
sub for t
y = usinθ( x ) -1/2g( x )²
(ucosθ) (ucosθ)²
tan = sinθ
cosθ
y=xtanθ - gx²
2(u²)(Cos²θ)(
Maximum Height (H)
The distance between the highest point reached and the horizontal plane through the point of projection
v² = u² - 2gH
@ Hmax v = 0
0² = u² - 2gH
uy = usinθ
u² = 2gH
(usinθ)² = 2gH
u²sin²(θ) = 2gH
Hmax = u²sin²(θ)
2g
Time of Flight (T)
Time taken by the projectile to move from its initial position to the final position along its path
v = u -gt, v=0 T = 2t
0 = u -gt -T = 2usin(2θ)
u = gt g
usinθ = gt
t = usinθ
Horizontal Range(R)
The distance from the initial to the final position of the projection
R = uTcosθ, T = 2usinθ
g
R = u2usinθ*cosθ
g
R = u²sinθcosθ
g
(sin(A + B) =sinAcosB + cosAsinB)
(sin(θ + θ) =sinθcosθ + cosθsinθ)
sin2θ = 2sinθcosθ
R = U²Sin(2θ)
g
