Physics 3.4

Physics 3.4 - Mechanical Systems

Vector

Vector

A quantity with both magnitude and direction, represented by an arrow.

Scalar

A quantity with only magnitude and no direction.

Momentum

The quantity of motion an object possesses, the product of mass and velocity.

Force

A push or pull acting on an object, causing it to accelerate.

Centre of Mass

The point where the mass of an object or system can be considered to be concentrated.

Acceleration

The rate of change of velocity

Impulse

A change in momentum

Displacement

Distance travelled in a given direction. Vector quantity

Net force

A resultant force that results in a change of motion

Velocity

The rate of change of displacement

Mass

The amount of matter in an object

Metres per second ($m\space{s}^{-1}$)

Unit for velocity

Metres per second squared ($m\space{s}^{-2}$)

Unit for acceleration

Newton (N)

Unit for force

Joule (J)

Unit for energy

Kilogram metres per second ($kg\space{m}\space{s}^{-1}$)

Unit for momentum

Newton metre (Nm)

Unit for torque

Balanced forces

Resultant force is zero, so no change in motion occurs

Centripetal acceleration

Acceleration towards the centre of a circle

Centripetal force

Force acting towards the centre of a circle that causes objects to travel in a circular path

Gravitational potential energy

Energy that an object has stored due to its position and the influence of gravity

Kinetic energy

Energy contained in a moving object

Newton’s first law

An object will not change its motion unless acted on by and external net force

Newton’s second law

F=ma

Newton’s third law

Every action has an equal and opposite reaction

Newton’s law of gravitation

$F=\frac{m_1m_2G}{r²}$　

Power

The rate at which energy is transferred

Watt (W)

Unit for power

Tension

Force along a string, rope or chain that is pulled tightly

Universal gravitational constant

$6.67×10^{-11}$$N\space{m²}\space{kg}^{-2}$

Work

When a force moves an object over a distance

Vertical circular motion

Circular motion where the kinetic and gravitational kinetic energies are constantly changing

Horizontal circular motion

Circular motion where the kinetic and gravitational potential energy remain constant

Too fast around a banked corner

Travel to the outside of the corner

Too slow around a banked corner

Travel to the inside of the corner

Critical speed

Ideal speed to travel around a banked corner, where $F_c=F_H$

Angular acceleration

Rate of change of angular velocity

Radians per second squared ($rad\space{s}^{-2}$)

Unit for angular acceleration

Angular displacement

The angle that an object has rotated through

Radians (rad)

Unit for angular displacement

Angular velocity

Rate of change of angular displacement

Radians per second ($rad\space{s}^{-1}$)

Unit for angular velocity

Convert translational to angular displacement

$d=r\theta$

Convert translational to angular velocity

$v=r\omega$

Convert translational to angular acceleration

$a=r\alpha$

Torque

A force that causes an object to rotate

Rotational inertia

A measure of an object’s resistance to changes in rotational motion

Kilogram metres squared ($kg\space{m}{s}²$)

Unit for rotational inertia

Angular momentum

Product of rotational inertia and angular velocity

Pure rotational motion

An object is only moving rotationally, with no translational motion

Pure translational motion

An object is only moving translationally, with no rotational motion

Conservation of energy in rotating systems

$E_T=E_{trans}+E_{rot}$

Objects with higher rotational inertia have ____ translational kinetic energy

Lower

Objects with lower rotational inertia have ____ rotational kinetic energy

Lower

Objects with lower rotational inertia have _____ translational kinetic energy

Higher

Objects with higher rotational inertia have ____ rotational kinetic energy

Higher

Translational kinetic energy

$\frac{1}{2}mv²$

Rotational kinetic energy

$\frac{1}{2}I\omega²$

Relationship between linear and rotational momentum

$I\omega=mvr, L=pr$

When the rotational inertia is changed…

Work has been done on the system

Amplitude

The distance from the equilibrium position

Angular frequency

The frequency of a steadily recurring phenomenon

Damping

As object lose energy when oscillating, the amplitude decreases over time. Period and angular frequency remain the same

Frequency

The rate at which something occurs over a period of time

Forced SHM

Driving forces are used to increase the amplitude of an oscillation

Driving forces

Forces with an equal or very similar frequency (the natural or resonant frequency) are applied to an oscillating object to increase its amplitude

Resonant frequency

The natural frequency of a system

Period

The time between occurances

Phasor

A line used to represent an oscillating quantity as a vector

Restoring force

The force acting in the opposite direction of motion to restore the oscillating object to its equilibrium position

Hooke’s Law

F=-ky

Newtons per metre ($N\space{m}^{-1}$)

Unit for spring constant

Relationship between period and frequency

$T=\frac{1}{f}$

Time period in simple pendulum

$T=2\pi\sqrt{\frac{l}{g}}$

Time period in spring

$T=2\pi\sqrt{\frac{m}{k}}$

Relationship between frequency and time period

$f=\frac{1}{T}$

Relationship between angular frequency and time period

$\omega=\frac{2\pi}{T}$

Angle where SHM occurs

<15 degrees either side of equilibrium position

Geostationary satellite

Satellite that orbits Earth vertically above the same position. Time period is 24 hours

Energy in SHM

Total energy = maximum kinetic or potential energy. Transfers between kinetic and potential energy, with equal amounts of each at the equilibrium position