Topic 2

Front 1

Velocity

Back 1

The rate of change of a particles position r:

v = dr/dt

The velocity and position are vectors, with both direction and magnitude. the magnitude of the velocity is the speed, v

Front 2

Scalar physical property

Back 2

(Such as temperature) in general varies through space and is represented by a single value at each point of space

Front 3

Vector physical property

Back 3

(Such as electric field strength) also varies through space, but in general has a different direction as well as a different magnitude at each point

Front 4

Velocity in 3D

Back 4

v = vxi + vyj + vzk

Where i,j,k are unit vectors, vectors of magnitude 1, pointing along the positive directions on the x, y, z axes and vx, vy, vz are the components of the vector on each axis. The magnitude of the vector is denoted v or |v| and is given by

V=(Vx^2 + Vy^2 + Vz^2)^1/2

The vector makes an angle theta with the z-axis and an angle phi to the x-axis in the xy-plane.

Vx=V sin(theta) cos(phi)= V (opp/V) (adj/V)= opp (adj/V)

Vy=V sin(theta) sin(phi)= V (opp(theta)/V) (opp(phi)/V)= (opp(theta)*opp(phi))/V

Vz=V cos(theta)= V adj/V = adj

And therefore:

Theta = arccos(Vz/V)

Phi = arctan(Vy/Vx)

Hint 4

Front 5

Vector addition, subtraction, and multiplication

Back 5

Consider the two vectors

u=uxi + uyj + uzk

v=vxi + vyj + vzk

Addition:

v+u=(vx+ux)i + (vy+uy)j + (vz+uz)k

Subtraction:

v+u=(vx-ux)i + (vy-uy)j + (vz-uz)k

Multiplication:

The scalar product or the dot product.

u.v=uxvx + uyvy + uzvz

Front 6

Linear Velocity

Back 6

Back (Definition)

Front 7

Angular Momentum

Back 7

Back (Definition)

Front 8

Moment of Inertia

Back 8

Back (Definition)

Front 9

mu =atomic mass constant

Back 9

1.66054 X 10^-27 kg

Front 10

Newton’s second Law of motion

Back 10

The rate of change of momentum is equal to the force acting no the particle.

dp/dt = F

1N = 1kg m s^-2

Because p=m(dr/dt)

dp/dt=d(m(dr/dt))/dt=

m(d^2r/dt)/dt=m(d^2r/dt^2)=

ma=F

Front 11

Harmonic Oscillator

Back 11

Back (Definition)

Front 12

Torque

Back 12

The acceleration of a rotation

dJ/dt=T

J=angular momentum= Iw

I= moment of inertia

w=angular velocity

Front 13

Analogies between translational and rotational

Back 13

Back (Definition)

Front 14

Work

Back 14

w, is done in order to achieve motion against an opposing force. For an infinitesimal displacement through ds (a vec- tor)

dw=-F*ds

where F⋅ds is the ‘scalar product’ of the vectors F and ds

F*ds=Fxdx+Fydy+Fzdz

For motion in one dimension, we write dw=–Fxdx. The total work done along a path is the integral of this expression, allowing for the possibility that F changes in direction and magnitude at each point of the path. With force in newtons and distance in metres, the units of work are joules (J), with

1J=1Nm=1kgm2 s−2

Front 15

The work of stretching a bond

Back 15

Back (Definition)