Section 1: Mechanics Flashcards
What are dimensions
Physical nature of quantity
Each dimension can have many diff units
Basic dimensions used in mechanical analysis
Length [L]
Time [T]
Mass [M]
SI units
Length: metre (m)
Time: second (s)
Mass: kilogram (kg)
Orders of magnitude: 10^x
giga; G; 10^9 mega; M; 10^6 kilo; k; 10^3 centi; c; 10^-2 milli; m; 10^-3 micro; µ; 10^-6 nano; n; 10^-9 pico; p; 10^-12
Scalars vs vectors
Scalars are quantities that only have a magnitude (no direction)
Vectors are quantities that have a magnitude and a direction
Negative of a vector e.g. -A
In the opposite direction to A
Vector multipled by scalar
Gives a vector in the same direction with scalar times the magnitude
If multipled by negative scalar, direction is reversed
Uniform motion
Motion in a straight line where the distance covered in any two equal time intervals is the same (i.e. constant speed)
Displacement
The distance moved in some direction
Both distance moved and direction are important
Units: m
Speed vs velocity
Speed: the distance covered per unit time (irrespective of distance)
Velocity: the displacement per unit time
Instantaneous velocity: the slope of the displacement-time graph at any particular instant
Units: m s^-1
Acceleration
Average acceleration: average rate of change of velocity over a time interval
Instantaneous acceleration: the slope of the velocity-time graph at any particular instant
Units: m s^-2
Galileo theory
In the absence of any forces, this is the property of a moving object to continue moving in a straight line at constant speed (i.e. constant velocity)
Projectile motion
The two components (horizontal and vertical) of the motion of a projectile are independent of one another
What is a projectile
Any body projected above the surface of the earth that is unpowered
Only force on the object is gravity once it’s projected
What does v(AB) mean
The velocity of observer A with respect to observer B (i.e. the velocity that B sees A moving with)
Frame of reference
A coordinate system where the observer is at rest with respect to the coordinate system
v(wind)
Air with respect to ground
Centripetal acceleration
An object moving at constant speed (v) in a circle has an acceleration towards the centre of the circle
Inertial coordinate system / reference frame
Any reference frame that moves with constant velocity, i.e. no acceleration
Newton’s 1st law
In the absence of any external forces, when viewed from a reference frame, an object at rest remains at rest, and an object in motion continues in motion with constant velocity
i.e. F = ma
Newton’s 2nd law
In an inertial reference frame, the acceleration on an object is equal to the net force on the object divided by the mass
i.e. a = Fnet/m
Newton’s 3rd law
If a system A exerts a force on another system B, then B exerts a force of the same magnitude A, but in the opposite direction
i. e. F(A on B) = -F(B on A)
* note: these forces act on diff systems
Reaction force AKA…
Normal force
Static friction force
No motion (sliding) involved
Kinetic friction
Arises when one surface slides along a second surface
Isolated system
Doesn’t interact with other systems, so no energy number comes in or goes out of the system
Total energy in isolated systems
A number that always remains the same
Energy is measured in ____
Joules (J)
Kinetic energy number (KE)
The energy number some object has because it’s moving
Potential energy number (PE)
The energy number an object has ‘stored’
Can be stored in many diff ways, e.g. gravitational and elastic
Total energy number = ?
KE number + PE number
Work
The change in the energy of a system resulting from the application of a force acting over a distance
Power
The rate at which work is done, i.e. the rate at which energy is transformed from 1 form to another
1 W = ?
1 J/s
+ve vs -ve values of work
+ve means work is done on the mass, i.e. KE of mass has increased
-ve means energy is being transferred out of mass, i.e. KE of mass has decreased
Conservation of momentum
The total momentum of a system remains constant as long as the net external force on the system is zero
Momentum - units
kg m/s Vector quantity (has direction)
