Theme A. Space, Time and Motion

Velocity

Change in displacement over time

Acceleration

Change in velocity over time

S.U.V.A.T. Equations

Vectors

Normal Force

The Force applied is mass times acceleration.

Weight

Density

The density of an object is the mass per unit volume.

Buoyancy Force

Spring Constant

Hooke’s Law

Static Friction

The friction force experienced when the object is at rest.

Dynamic Friction

The friction force experienced when the object is in motion.

Viscous Drag

The drag force experienced by a solid sphere in a fluid

Linear Velocity

Angular Velocity

Angular Acceleration

Centripetal Force

Impulse

Elastic Collisions

All Kinetic Energy and Momentum of one object passes to the colliding object (Kinetic Energy is conserved).

Inelastic Collisions

Kinetic Energy is not conserved in the collision.

Explosions

The momentum of the projectile is equal and opposite to the momentum of the firing device (recoil).

Work

The work done on an object is the force applied to move the object in the direction of the force.

Kinetic Energy

The kinetic energy is the energy stored in the body when it is in a state of motion.

Gravitational Potential Energy

The gravitational potential energy is the energy stored in a body due to the effects of gravity.

Elastic Potential Energy

The elastic potential energy is the energy stored in any elastic body i.e. a body that returns to its original shape after the external force is removed.

Conservation of Energy

Kinetic Energy = Potential Energy

Power

The work done per unit time

Power needed to maintain a constant velocity

Efficiency

Energy Density

Torque (in formula booklet)

A measure of the rotational force applied to an object, calculated as the product of the force and the distance from the pivot point.

Couple

A couple is a pair of equal-sized forces that have different lines of action but are parallel to each other and act in opposite directions, either side of the axis of rotation.

Angular Displacement, Velocity and Acceleration

The change in angular position of a rotating object, measured in radians. Angular velocity is the rate of change of angular displacement, while angular acceleration is the rate of change of angular velocity.

Angular S.U.V.A.T. Equations

A set of equations that relate angular displacement, angular velocity, angular acceleration, and time for rotational motion, similar to linear S.U.V.A.T. equations.

Moment of Inertia

A measure of an object's resistance to changes in its rotation, calculated as the sum of the products of each mass element and the square of its distance from the axis of rotation.

Moment of Solid Cylinder, Disk or Ring

Moment of Solid Sphere

Second Law of Rotational Motion

Angular Momentum

The angular momentum of any closed/isolated system is conserved if there is no resultant torque.

Angular Impulse

Rotational Kinetic Energy

Conservation of Energy down a Slope

1 Revolution per Second in Rad/s

Reference Frame

A reference frame is a set of coordinate axes and clocks at all points in space. A non-accelerating frame is called an inertial frame of reference.

Galilean Distance Transformation

Galilean Velocity Transformation

Galilean Time Transformation

Postulates of Special Relativity

• All laws of physics remain the same in all inertial frames.

• The speed of light in a vacuum is constant in all frames.

Lorentz Factor

Relativistic Distance Transformation

Relativistic Velocity Transformation

Relativistic Time Transformation

Spacetime Interval

Spacetime Coordinate Differences

Distance Relation

Time Relation

Time Dilation

Length Contraction

Proper time and Proper Length

• A proper time interval is the time between two events that take place at the same point in space.

• A proper length is the length measured when the object is at rest. The object's rest frame is the reference frame where the object is at rest. Only the lengths in the direction of motion are contracted.

Simultaneity

If two events occur simultaneously in frame S’ with a time interval of 0, then the following equation is the time interval in frame S.

If x' = 0, the events will not be simultaneous in other frames.

If x = 0 i.e. the simultaneous events occur at the same point in space, thus they are simultaneous in all frames of reference.

Angle of the Wordline

The angle of the wordline cannot exceed 45^o.

Angle of Moving Frame

The angle of the moving frame cannot exceed 45^o.

Causation in Spacetime Diagrams

An event ‘E’ can cause event ‘L’ if the time separating ‘E’ and ‘L’ is greater than or equal to the travel time of a photon from the position of ‘E’ to ‘L’.

Scale Relation of Axes in Different Frames

Length Contraction in Spacetime Diagrams

• Draw a line parallel to the (ct)’ axis at the start and end of the length in the moving frame and extrapolate it towards the x-axis in the stationary frame to find the proper length.

• Draw a line parallel to the (ct) axis at the start and end of the length in the stationary frame and extrapolate it towards the (x’)-axis in the moving frame to find the contracted length. 

• Lengths are only contracted when in the direction of the velocity.

Time Dilation in Spacetime Diagrams

• Draw a line parallel to the x-axis from the start and end points of (ct)’ in the moving frame and extrapolate it towards the (ct) axis to find the proper time.

• Draw a line parallel to the (x’)-axis from the start and end points of (ct) in the stationary frame and extrapolate it towards the (ct)’ axis to find the dilated time.

Simultaneity in Spacetime Diagrams