Newton to Einstein Flashcards
Define the unit Vector
The unit vector is a vector with a magnitude of one. Any vector is made into its corresponding unit vector by dividing it by its magnitude.
Define the Dot Product
C = a . b = |a||b|cos(x) , where x is the angle between a and b when they are ‘tail to tail’
Define the cross product
C = a X b = |a||b|sin(x) , where x is the angle from a to b. C is a vector perpendicular to both a and b, its direction depends on the order a and b are crossed.
Define the term Kinematics
Kinematics is the study of the relationship between an object’s position, speed and acceleration.
Define average velocity
Average velocity is the ratio between the displacement S and the time interval Δt in which the displacement occurs. V = S/Δt
Define instantaneous velocity
Instantaneous velocity is the velocity as Δt -> 0. It reaches a limiting value which describes the rate of change of displacement at time t. V = dS/dt
Define constant velocity
An object moving with constant velocity will cover equal displacements in equal intervals of time. The magnitude and direction of the velocity will also be constant.
Define acceleration
Acceleration is the rate of change of velocity.
Express the position of an object as a position vector in terms of its constituent vectors parallel to x and y.
r = xi +yj
Express the velocity of an object as a vector in terms of its constituent vectors parallel to x and y.
v ̅=ⅆx/ⅆt i ̂+ⅆy/ⅆt j ̂ = vxi + vyj
Express the instantaneous acceleration of an object as a vector in terms of its constituent vectors parallel to x and y.
a = ⅆv/dt = (ⅆv_x)/ⅆt i ̂+(ⅆv_y)/ⅆt j ̂
What is the defining characteristic of projectile motion, excluding air resistance.
Acceleration parallel to y only.
Define angular displacement
Final Θ - Initial Θ
Define angular velocity ω
ω = dΘ/dt
Rate of change of angular displacement
Define angular acceleration (alpha)
Rate of change of angular velocity
What are the respective signs of angular velocity for acw motion and cw motion
ω > 0 for acw motion , ω < 0 for cw motion
What are the defining characteristics of uniform circular motion
ω is constant and therefore ⅆθ/ⅆt is constant. |ω| = 2Π/T where T is the period. However, the direction of motion is constantly changing.
Define velocity for uniform circular motion
Because ω is constant, ⅆω/ⅆt = α = 0, the acceleration α is zero tangential to the motion of the particle.
v = ⅆS/ⅆt = ⅆ(rθ)/ⅆt therefore v = r ⅆθ/ⅆt = r ω
v = r ω
What Force is responsible for the circular motion of an object.
Centripetal Force given by:
F = mv^2 / r
What is the characteristic feature of centripetal acceleration
It is always perpendicular to the velocity of an object exhibiting circular motion
Define Centripetal Accelerstion
|a|= ω^2 r = v^2 / r
Define the principle of superposition of forces
The net force on an object is the vector sum of the forces acting on it.
Give the relationship between angular acceleration and tangential acceleration
alpha = a_t / r