Monthly Archives: March 2018
Kinematics – Motion in a plane
1. A coordinate system provides a systematic means of specifying the position of a particle. A system in one dimension involves choosing an origin and a positive direction in which values of the position coordinate increase. Values of the position coordinate are positive or negative numbers multiplied by an appropriate unit of length, usually the SI unit of length, the metre (m).
2. The movement of a particle along a line can be described graphically by plotting values of the particle’s position x, against the corresponding times t, to produce a positiontime graph. Alternatively, by choosing an appropriate reference position x_{ref}and defining the displacement from that point by s_{x} = x − x _{ref}, the motion may be described by means of a displacementtime graph.
3. Uniform motion along a line is characterised by a straightline positiontime graph that may be described by the equation
where v_{x} and x_{0} are constants. Physically, v_{x} represents the particle’s velocity, the rate of change of its position with respect to time, and is determined by the gradient of the positiontime graph
x_{0} represents the particle’s initial position, its position at t = 0, and is determined by the intercept of the positiontime graph, the value of x at which the plotted line crosses the xaxis, provided that axis has been drawn through t = 0.
4. Nonuniform motion along a line is characterised by a positiontime graph that is not a straight line. In such circumstances the rate of change of position with respect to time may vary from moment to moment and defines the instantaneous velocity. Its value at any particular time is determined by the gradient of the tangent to the positiontime graph at that time.
5. More generally, if the position of a particle varies with time in the way described by a function x(t), then the way in which the (instantaneous) velocity varies with time will be described by the associated derived function or derivative
6. The instantaneous acceleration is the rate of change of the instantaneous velocity with respect to time. Its value at any time is determined by the gradient of the tangent to the velocitytime graph at that time. More generally, the way in which the (instantaneous) acceleration varies with time will be described by the derivative of the function that describes the instantaneous velocity, or, equivalently, the second derivative of the function that describes the position:
7. Results and rules relating to differentiation and the determination of derivatives are contained in Table 6. The derivative of a constant is zero, the derivative of f(y) = Ay^{n} is df/dy = nAy^{n} ^{−1}.
8. The signed area under a velocitytime graph, between specified values of time, represents the change in position of the particle during that interval.
9. Uniformly accelerated motion is a special case of nonuniform motion characterised by a constant value of the acceleration, a_{x} = constant. In such circumstances the velocity is a linear function of time (v_{x}(t) = u_{x} + a_{x}t), and the position is a quadratic function of time ().
10. The most widely used equations describing uniformly accelerated motion are
11. Position x, displacement s_{x}, velocity v _{x }, and acceleration, a_{x}, are all signed quantities that may be positive or negative, depending on the associated direction. The magnitude of each of these quantities is a positive quantity that is devoid of directional information. The magnitude of the displacement of one point from another, s = s_{x}, represents the distance between those two points, while the magnitude of a particle’s velocity, v = v_{x}, represents the speed of the particle. The magnitude of the acceleration due to gravity is represented by the symbol g, and has the approximate value 9.81 m s^{−2} across much of the Earth’s surface.
Kinematics – Motion in a straight line motion equations
1. The most widely used equations describing uniformly accelerated motion in a straight line along a horizontal surface, which is taken as along the xaxis are:
Note: Position x, displacement s_{x}, velocity v _{x }, and acceleration, a_{x}, are all signed quantities that may be positive or negative, depending on the associated direction.
For example, an object travelling at 10 m/s East, its initial velocity, u _{x } = +10 m/s as its direction, East is taken as the positive direction. After 2 seconds, this object then traveled at 30 m/s West, its final velocity will be taken as, v _{x} = – 30 m/s, as its direction, West is taken as the negative direction.
2. Another most widely used equations describing uniformly accelerated motion in a straight line of an object thrown upwards or dropped downwards perpendicular to the surface, which is taken as along the yaxis are:
Note: Position y, displacement s y, velocity v _{y }, and acceleration, a_{y}, are all signed quantities that may be positive or negative, depending on the associated direction.
For example, an object travelling 10 m/s downwards, its initial velocity, u _{x } = 10 m/s as its direction, downward direction is taken as the negative direction. After 2 seconds, this object then traveled at 30 m/s downwards, its final velocity will be taken as, v _{x} = 30 m/s, as its direction, downwards is taken as the negative direction.
The magnitude of the acceleration due to gravity is represented by the symbol g, and if it has a value 9.8 m s^{−2} (in the formula sheet near the Earth surface). Since the downward direction is negative, then the acceleration due to gravity = – 9.8 m s^{−2 }
Protected: Physics Kinematics – Motion equations and vectors
Stem – 3D printing for 4 by 4
3 D printing
https://www.simplify3d.com/support/materialsguide/

ABS
ABS is a low cost material, great for printing tough and durable parts that can withstand high temperatures. 
Flexible
Flexible filaments, commonly referred to as TPE or TPU, are known for their elasticity allowing the material to easily stretch and bend. 
PLA
PLA is the goto material for most users due to its easeofuse, dimensional accuracy, and low cost.