Physics: Motion, Scalars, and Gears

• A vector has magnitude and direction.
• A scalar has just magnitude.
• Scalars are generally not negative, but vectors can be positive or negative, as direction can be positive or negative.

Examples of Scalar and Vector Quantities

• Speed is a scalar quantity.
• Velocity is a vector quantity.
• Distance is a scalar quantity.
• Displacement is a vector quantity.
• Time is a scalar quantity.
• Momentum is a vector quantity.
• Acceleration is a vector quantity.
• Energy is a scalar quantity.
• Force is a vector quantity.
• Mass is a scalar quantity.

Displacement Example

• For a ball thrown off a cliff, displacement is zero at the height of the cliff.
• Above the cliff, the ball has positive displacement; below, it has negative displacement.
• The "0" point of a vector can be set, such as setting the bottom of the cliff as zero so the ball never has negative displacement.
• Speed becomes velocity when direction is given.
• Being thrown 10ms⁻¹ is speed, while being thrown 10ms⁻¹ at a 30° angle is velocity.

Acceleration Example

• A car traveling around a roundabout at constant speed is accelerating.
• Constant speed means its direction is constantly changing.
• Constantly changing direction means its velocity is constantly changing.

Vectors

• Vectors are represented by arrows.
• The size/length of the arrow represents the vector magnitude.

Object Interaction

• A force is a push or pull that acts on an object due to interaction with another object.
• All forces between objects are either contact or non-contact.

Non-Contact Forces

• Non-contact forces occur when objects are physically separated.
• Electrostatic forces are a type of non-contact force caused by attraction or repulsion of charges.
• Gravitational attraction is another type of non-contact force.
• Mass creates a force of attraction.

Contact Forces

• Contact forces occur when objects are physically touching.
• Normal contact force is felt in the opposite direction to contact.
• The force is normal to the planes of contact.
• Friction is a contact force caused by surfaces and their roughness when moved in contact.

Gravity

• All matter has a gravitational field.
• All matter attracts all other matter.
• The larger the mass, the stronger the field, and the greater the attraction.

Weight

• Weight is the force exerted on a mass by the gravitational field, measured in Newtons.
• Calculate weight using: weight = mass × gravitational field strength.
• W = mg = m × 10
• W is weight in newtons (N) and m is mass in kilograms (kg).
• Use a force meter (calibrated spring-balance) to measure the weight.
• A weighing scale measures the force exerted, and then divides by 10 to give mass.
• The gravitational field strength on Earth is 9.8.
• A person's mass is the same on different planets, but their weight will be will be different.
• The gravitational field strength, g, will be planet dependent
• Acceleration in free fall is due to gravity, and is the same as g, i.e., 10ms⁻².
• The weight of an object is considered to act at the object's centre of mass.

Resultant Force

• Resultant force is a single force representing the sum of all forces acting on an object.
• If more than one force act along a straight line, the resultant can be found by adding (acting in the same direction) or subtracting (acting in opposite directions) them.

Skydiver Example

• The forces that act on a skydiver are air resistance and weight.
• Initially, the skydiver has no air resistance.
• The only force acting is weight.
• As the skydiver falls, they accelerate, increasing speed.
• Net force is simply 833N down.
• As air resistance increases, the resultant force from weight decreases: Resultant is 833 - 350 = 483N down.
• Acceleration decreases, so there is less speed gained as quickly: Resultant is 133N down.
• Eventually, forces are equal and balanced, so there is no resultant force.
• Resultant = 0 Newton.
• Because there is no acceleration when the resultant force is 0, the skydiver travels at terminal velocity.
• Free Body Diagrams show the forces, and directions acting on an object, like the skydiver.

Resolving Forces

• A force F at angle θ to the ground can be resolved parallel and perpendicular to the ground components.
• Using Pythagoras' Rule, the two components are F² = (Fcosθ)² + (Fsinθ)².

Work Done

• Calculate Work Done using the formula: Work Done = Force × Distance.
• W = Fs, where Work Done, W, is in joules (J), force, F is in newtons (N), and distance, s, is in metres (m).
• The distance is the distance moved along the line of action of the force.
• Work transfers energy from the object doing the work to another form.
• If a book is lifted 1m in the air, and 2m to the right, work is done when moving 1m vertically, as that is in the direction of the force (gravity).
• Energy is transferred from muscles to the book, increasing its gravitational potential when lifted.
• One joule of work is done when a force of one newton causes a displacement of one metre.
• 1 joule = 1 newton-metre
• Work done against frictional forces causes a rise in the temperature of the object.

Springs

• To stretch, bend, or compress an object, more than one force has to be applied.
• If a single force is applied to an object, it will just move in that direction, not deform it.
• If it is pulled in opposite directions, it will stretch.
• If it is fixed at one point and stretched, a force is still being applied by the fixed point where it is attached.
• Deformation means changing the shape, and can either be elastic or plastic deformation.

Elastic Deformation

• The object returns to its original shape when the load has been removed.
• An example is an elastic band.

Plastic Deformation

• The object does not return to its original shape when the load has been removed.
• An example is a spring when pulled too far.

Hooke’s Law

• The extension of an elastic object, such as a spring, is directly proportional to the force applied.
• This only applies if the limit of proportionality is not exceeded.
• F = kx, where:
  • F is the force applied to the spring, measured in Newtons (N).
  • K is the spring constant, measured in Newton per metre (Nm⁻¹).
  • X is the extension, measured in metres (m).
• A linear line for a Force/Extension Graph is the elastic region.
• This is following Hooke's Law, and the gradient is k.
• The point at which it stops being linear is the limit of proportionality.
• From that point on, it does not obey Hooke's Law.
• The non-Linear line is where there is plastic behaviour as it is no longer following Hooke's Law.
• If shallow, a lot of extension will have not a lot of force, so it is easy to stretch.

Linear Graphs

• If the graph is linear, with no non-linear end section, the material is brittle and snaps instead of stretching after the elastic limit.

Work Done

• Calculate: Work Done = (1/2)kx².
• When a force stretches/compresses a spring, the spring does work, and elastic potential energy is stored in the spring.
• Providing it does not inelastically deform: the work done on the spring = the elastic potential energy stored.

Moments and Rotation

• Applies to objects attached to pivot points that can rotate but not move away.
• If a force is applied along a line passing through the pivot, the object does not rotate and is just held still.
• If there is a distance between the pivot and the line of action of the force, the object rotates about the pivot in the direction of the force applied.
• If the force is applied not perpendicular to the object, the perpendicular distance from the pivot to line of force needs to be taken into consideration.
• Moment of a Force = force × perpendicular distance
• M = Fd, where:
  • M is the moment of a force, measured in newton-metres (Nm).
  • F is the force measured in newtons (N).
  • d is the perpendicular distance from the pivot to the line of action of the force, measured in metres (m).
• Taking off a bike is an example of moments.
• pressing your foot down on the pedal causes a moment about the pivot, in turn moving the pedal arms.
• Equilibrium is when the sum of anticlockwise moments = sum of clockwise moments.

Levers and Gears

• Gears can change speed, force, or direction by rotation.
• If connected to a gear with fewer teeth (i.e. a smaller gear) the second gear will turn faster, but with less force, and in opposite direction to first gear.
• If connected to a gear with more teeth (i.e. a larger gear), it turns slower but has more force, and in the opposite direction.
• The second gear will always turn in the opposite direction.
• To increase power, a larger gear is used for the secondary gear.
• As the force on the red gear is further distance from its pivot, the momentum of the larger gear is greater.

Pressure

• Particles in a gas move randomly in every direction.
• Particles exert forces on the container they are in, which is felt as pressure.
• Pressure = force / area
• p = F / A, where:
  • p is pressure, measured in pascals (Pa).
  • F is force, measured in newtons (N).
  • A is area, measured in metres squared (m²).
• Pressure produces a net force at right angles to any surface.

Pressure in Fluids

• Whether an object floats or sinks depends on the weight of the object and the weight of the water it displaces.
• Objects float if its weight is less than the weight of the water it displaces.
• So a 1000kg boat will sink into the water until it has displaced 1000kg of water.
• Providing the boat doesn't completely submerge before it displaces this amount, then it will float.
• Pressure in a liquid varies with depth and density.
• Pressure leads to an upwards force on a partially submerged object which is buoyancy.
• The buoyancy force is the upwards force that counteracts the weight of the floating object.
• This is equal to the weight of the fluid displaced by the object.
• A ping pong ball floats on water because its density is less than the density of the water.
• For the volume displaced, the weight of the equivalent amount of water is greater than the weight of the ping pong ball, so the resultant force is buoyancy, so it floats.
• The greater the depth, the greater the weight of the water above you, the greater the force felt, which leads to greater pressure.
• Calculate pressure due to a column of liquid: height of column × density of liquid × g.
• p = hρg,

Variables

• p is pressure in pascals (Pa).
• h is the height of the column in metres (m).
• ρ is the density in kilograms per metre cubed (kg/m³).
• g is the gravitational field strength in newtons per kilogram (N/kg).
• N/kg is normally 10 on Earth.
• Upthrust, upward force occurs because a partially or totally submerged object experiences a greater pressure on the bottom surface than on the top surface.

Atmosphere

• The Earth's atmosphere is a thin layer (relative to size of the earth) of air around the Earth.
• The atmosphere gets less dense with increasing altitude.
• This is because the air density is the total weight of the air above an area.
• The weight of the air is the force which causes the pressure.
• At higher elevations, there are fewer air molecules above the unit area than the same area at lower heights, which leads to a smaller weight and less pressure.

Idealised Assumptions

• Isothermal: all is at the same temperature
• Transparent to solar radiation
• Opaque to terrestrial radiation

Distance

• Distance is how far an object moves.
• Distance does not involve direction and is therefore a scalar quantity.

Displacement

• Displacement includes both distance (an object moves) and direction.
• It is measured in a straight line from the start point to the finish point.
• Displacement is a vector quantity.

Speed

• Speed does not involve direction and is a scalar quantity.

Velocity

• Velocity which is a vector quantity, is speed in a given direction.
• If an object travels in a circular motion, the object constantly changes direction.
• Velocity which is a vector that depends on movement/direction, is constantly changing.
• A change in velocity is defined as acceleration, so although the object isn't speeding up, it is accelerating due to the changing direction.
• The speed of a moving object is rarely constant.

Typical speeds

• Wind = 5-7ms⁻¹
• Sound = 330ms⁻¹
• Walking = ~ 1.5ms⁻¹
• Running = ~3ms⁻¹
• Cycling = ~6ms⁻¹
• Bus = 14km/h
• Train = 125miles/h
• Plane = 900km/h

Units

• Distance measured in mm, cm, m and km.
• Time is measured in units of ms, s, mins and hours.
• Use appropriate depending on lengths involved.

Calculating Speed

• Speed = distance / time
• v = d/t
• Remember to convert units to make sure everything is equivalent.

Non-Uniform Motion

• Work out TOTAL TIME and TOTAL DISTANCE for average speed.
• Then use: average speed = total distance / total time.
• For different speeds to travel distances work out total time, distance / speed to work out total time, then sum the various distance.

Displacement Time Graphs

• Gradient is velocity.
• A sharper gradient means faster speed.
• Negative gradient means returning back to starting point.
• Horizontal line means stationary.
• 0 Distance means that it is back to starting point.
• Area under line = nothing
• Speed = nothing.
• Curved Line means that the velocity is changing which is acceleration.
• If an object is accelerating, its speed can be determined by drawing a tangent and calculating the gradient of the distance-time graph.

Velocity-Time Graphs

• Gradient is acceleration.
• Sharper gradient means greater acceleration.
• Negative gradient is deceleration.
• Horizontal line means constant speed.
• 0 Velocity means that it is stationary.
• As the line is at 0.0 the object is stationary.
• Area under line = distance travelled.
• Sometimes counting the squares is the best method for a curved line.
• Curved Line means that the acceleration is changing.

Average Speed

• This is for when the speed changes during the motion.
• Use overall distances and timings to work out average speed.

Falling in a Fluid

• Initially, the object will fall freely under gravity (9.8 m/s²).
• However drag forces will act (see skydiver).
• Gradually the drag force increases until terminal velocity is achieved.
• Acceleration decreases as drag increases, until no acceleration at terminal velocity.
• ~40ms⁻¹ In this case.

Calculations

• Average Speed = Total Distance / Total Time.
• a = (v - u) / t.
• v² = u² + 2as.
• Kinetic Energy = (1/2)mv².

Newton's First Law

• Objects have a constant velocity unless acted on by a resultant force.
• If a resultant force acts on the object, it will accelerate.
  • Acceleration is change in velocity over time.

Velocity Changes

• The velocity will change.
• Either the direction or speed of the object will change (or both).
• If no resultant force acts on the object, and the object is stationary it will remain stationary.
• If no resultant force acts on the object, and the object is moving it will continue to move at the same velocity.
• The tendency for objects to continue in uniform velocity (or stay at rest) is inertia.

Newton's Second Law

• The acceleration of an object is proportional to the resultant force acting on the object, and inversely proportional to the mass of the object.
• Force = mass x acceleration
• F = ma, where F is the force in newtons N, m is the mass in kg and a is the acceleration in m/s².

Inertia

• The inertia of an object is the measure of how difficult it is to change the velocity of an object.
• Inertial mass = force / acceleration f/a.

Newton’s Third Law

• Whenever two objects interact, the forces they exert on each other are equal and opposite.
• Rocket taking off.
  • The rocket exerts a force on the gases being ejected; these forces are the same but in equal and opposite directions, causing the rocket to lift off the ground.
• A book on a table.
• The weight of the book from the Earth = the pull of the book on the Earth.

Vehicle Stopping Distances

• After seeing a hazard
• Before you react, during reaction time you travel a distance.
  • Thinking Distance
• Then you react, causing the car to slow down and stop over a distance.
  • Braking Distance

Distances

• Stopping distance = total of thinking + braking distances.
• Thinking Distance factors:
  • Speed
  • Affected by reaction time
  • Concentration
  • Tiredness
  • Distractions
  • Influence of drugs/alcohol
• Braking Distance factors:
  • Speed
  • Poor road conditions (icy, wet)
  • Bald tires (low friction)
  • Worn brake pads
  • Weight (more passengers)

Speed and Braking

• Greater the speed, the greater distance travelled during the same time as well as increased reaction time
• Measure reaction times by the "ruler drop”, and the time it takes to catch it (S).
• Measured by; S = ut + 1/2 at², where U = 0, A =G so t = √2gs.
• S means the distance from ruler, travelling through the hand.

Breaking Forces on Vehicles

• When a force is applied to the brakes of a vehicle. The vehicle’s kinetic energy decreases/ reduces, and the temperature of the breaks increase (Brakes by friction onto the wheel). If speed is greater, Breaking force for car over same distance, it Leads to breaks overheating due to dangerous acceleration.

Momentum

• Momentum = Mass x Velocity
• P = MV which P is momentum, mass and velocity, measured in Meters, Kilograms and Meters/second respectively. Momentum is always reversed in an Explosion and collision (Air residence, friction, electro static attraction). The Sum of total, and final momentum is reversed after explosions. So Two Marbles colliding, or The Vector Memorandum.

Change and Forces Effecting Momentum

• Force is equal to the Rate the Momentum changes known as Newton’s Second Law: Force = Change in a certain momentum, effected over time, as expressed as the Change = MV-MU/T. Large Declerations is dangerous and is a large change or force felt Passengers & Cars or (neck whiplash) Can explain that large Deceleration =Large change in momentum, due to the time over exerted onto an an object or persons over the full duration.

Safety Features

• Seat Belts Prevents momentum but stretches you, Increasing distance moved, though is slower the persons stop, as It Increases rated of change momentum whilst it reduces the forces.

Crumple Zones

• Can reduce acceleration/ force. Solid Metal Block car =Stop in crash- instead blows softening or crash= areas softer at the car;s front and compact from absorbing and deforming the energy; for a certain Time!

Air Bags

• Prevent head whiplash, upon inflated crashes= Your Head slows into increase time, stopping =Reduces force onto the person and neck to stop it.

Test your knowledge of physics concepts, including circular motion, speed vs. velocity, displacement, gear ratios, and scalar quantities. This quiz covers key principles in mechanics and motion.