Rigid Body Mechanics Flashcards
What is the prefix for each of the following:
- x10^12
- x10^9
- x10^6
- x10^3
- x10^2
- x10
x10^12 = T (tera) x10^9 = G (giga) x10^6 = M (mega) x10³ = k (kilo) x10² = h (hecto) x10 = da (deca)
What is the prefix for each of the following:
- x10^-1
- x10^-2
- x10^-3
- x10^-6
- x10^-9
- x1-^-12
x10⁻¹ = d (deci) x10^-2 = c (centi) x10^-3 = m (milli) x10^-6 = μ (micro) x10^-9 = n (nano) x1-^-12 = p (pico)
SI base unit for:
- length
- time
- weight
- angle
- temperature
- amount of substance
- electrical current
- luminosity
length - m time - s weight - kg angle - radian temperature - k amount of substance - mol electrical current - A luminosity - cd (luminous intensity)
7 scalar quantities?
distance speed angle rotation rate mass temperature energy
7 vector quantities?
displacement velocity angular displacement angular velocity force momentum acceleration
How to combine vectors by resolving?
Split into component parts of ‘up/down’ and ‘across’, then use pythagoras to work out the magnitude of the resultant vector, and trig to work out the angle
Why is a cartesian system said to be orthogonal?
The axes are all independent of one another - you can travel along one axis without changing position in the others
What is a plane?
A flat 2D surface, with zero thickness, encompassing 2 axes of a 3D co-ordinate system
3 rules about planes?
2 planes can be at right angles to each other
3 planes, but no more, can mutually be at right angles (e.g. corner of a cube)
A straight line is formed when 2 planes cross each other
What is the difference between cartesian and polar coordinates?
Cartesian uses 3 axes to describe the position of a point in 3D, so direction is not required as it is implied by the position already
(x, y, z)
Polar coordinates uses a distance and either 1 or 2 angles depending on whether it is describing a position in 2D or 3D
(r, θ, ϕ)
What is kinematics?
The study of motion, concerned only with the ways in which the object moves, not the cause of the movement (i.e. the force)
Explain degrees of freedom?
What is constrained movement?
A free object can move along 3 axes independently, called 3 translational degrees of freedom. It can also rotate around each of the 3 axes, termed 3 rotational degrees of freedom. Therefore, a free object is said to have 6 degrees of freedom as it can move in any way it chooses.
An object is said to have constrained movement if one or more of these degrees of freedom is restricted. For example, a ball on a pool table can rotate around any 3 axes, but can only move along 2 ( it can’t move up and down off the table), therefore it only has 2 translational degrees of freedom
How to work out average velocity?
How to work out instantaneous velocity?
Av vel = change in displacement/time
Instantaneous = gradient at that point in a displacement-time graph
How to work out average acceleration?
How to work out instantaneous acceleration?
Av acc = change in velocity /time
Instantaneous = gradient at that point in a velocity-time graph
What does the area under a velocity-time graph show?
Displacement
Symbol for:
Anglar acceleration?
Angular velocity?
Angular displacement?
α - angular acceleration
ω - angular velocity
θ - angular displacement
What is angular velocity?
Unit of angular velocity?
The angular displacement travelled by an object per second
Units = rad/s
How to work out average angular velocity?
How to work out instantaneous angular velocity?
Change in angular displacement/time
ω=Δθ/t
OR plot an angle-time graph and calculate the gradient
Instantaneous = plot an angle-time graph, work out the gradient of the tangent at that point
If plotting an angle-time graph, what value is given by:
- gradient?
- gradient of tangent to the curve
gradient = average angular velocity
gradient of tangent = instantaneous angular velocity
What is angular acceleration?
Units?
How to calculate average angular acceleration?
The rate of change of angular velocity
Its are rad/s²
Average = change in angular velocity/time α = Δω/t
Instantaneous = gradient of ‘angular velocity-time’ graph
What is statics?
Branch of mechanics dealing with forces and moments acting on bodies which are at rest, or moving with constant velocity - this may be constant angular and/or linear velocity
2 effects a force may have on a body?
A force can:
1 - alter the body’s state of motion
2 - deform the body’s shape
Simple device to measure force and how it works?
A spring balance may be used to measure the force exerted by a body.
It consists of a loaded spring inside a holder, with a calibrated scale printed on it. A hook at one end of the spring enables the application of a force, and this stretches the spring proportional to the magnitude of the force. The spring balance’s scale shows the magnitude of force acting parallel to the spring. The scale is usually in Newtons (N)
What is mass?
What is weight?
Mass = quantity of matter of which a body is composed (kg)
Weight = force of gravity acting on a body (N)