Concise Physics Handbook

The formula describes the motion of a body at a constant velocity. v is the velocity, equal to the ratio of path S to the time t taken. Coordinate x changes uniformly, depending on the initial position x₀ and velocity v.

The formula shows the distance traveled by a body in time t. This can be calculated as the difference between the final and initial coordinates (x − x₀), or as the product of constant velocity v and the time of motion. Only suitable for uniform motion.

Acceleration a shows how quickly the velocity of a body changes over a period of time. If the body accelerates or decelerates uniformly, then the change in velocity (Δv) is divided by the time interval (Δt), giving the acceleration in m/s².

The formula reflects the change in velocity v of a body over time. The initial velocity v₀ increases (or decreases) by the amount of acceleration a, multiplied by time t. The ± sign depends on whether the body is accelerating or decelerating.

This formula determines the position x of a body at any given time when moving with constant acceleration. The terms describe: the initial coordinate x₀, the contribution from the initial velocity v₀·t, and the contribution from acceleration, proportional to the square of time. It is applicable in the absence of resistance and with constant acceleration.

This formula describes the velocity of a body during free fall, starting with an initial velocity v₀, taking into account the acceleration due to gravity g and time t. The ± sign depends on the direction of motion: up or down.

The formula describes how the height of a body changes during vertical motion. The first term is the contribution of the initial vertical velocity, the second is the influence of gravitational acceleration. The ± sign depends on the direction of motion: upwards (decreasing height over time) or downwards (increasing height relative to the start).

The formula allows calculating the velocity v of a body without explicitly stating time — through its initial velocity v₀ and displacement height h. This is convenient when the fall height is known but the time is not. The ± sign depends on the direction: acceleration towards the ground or deceleration when rising.

The initial velocity v₀ of a body thrown at an angle α is broken down into two components: horizontal v₀ₓ and vertical v₀ᵧ. This allows treating the motion independently along the X and Y axes, simplifying calculations of trajectory and flight time.

The formula describes the horizontal distance traveled during the body's motion. Since there is no acceleration along the X-axis, the motion is uniform, and the path is calculated using the classical formula — velocity multiplied by time.

This formula determines the body's position at any given time after launch. The first part is the inertial ascent due to initial momentum, the second is the descent due to gravity. Together, they describe the parabolic trajectory.

This formula shows how long a body will ascend until it reaches its maximum height. At this point, the vertical velocity becomes zero. The greater the initial vertical velocity, the longer the ascent.

The maximum flight height is reached when the vertical velocity becomes zero. It depends on the initial vertical velocity and the acceleration due to gravity. The second version of the formula shows the dependence on the total initial momentum and the launch angle.

This formula shows how far from the launch point the body will land. It depends on the initial velocity, launch angle, and gravitational force. The sine of twice the angle determines the optimal angle for maximum range — 45°, all else being equal.

Frequency ν is the number of revolutions per second, inversely proportional to the period T of one revolution. The arc formula S shows the path traveled by a rotating body as the product of the angle of rotation Δφ (in radians) and the radius of the circle R.

Angular displacement Δφ shows the angle a body has rotated during circular motion. It is the difference between the final and initial angle values, measured in radians.

Angular velocity ω measures how fast a body rotates around an axis. It shows how many radians the body turns per unit of time. All three forms are equivalent and reveal the relationship between angular displacement, period, and rotational frequency.

Linear velocity v shows how fast a body moves along a circular trajectory. It can be expressed through distance over time, through angular displacement, or directly through angular velocity and radius. The formula combines rotational and translational motions.

Centripetal acceleration is directed towards the center of rotation and is necessary to maintain motion along a circular path. It depends on the square of the velocity (linear or angular) and is inversely proportional to the radius.

Angular acceleration ε describes how quickly the angular velocity of a rotating body changes. It is analogous to linear acceleration, but in the context of rotational motion — and depends on the change in angular velocity over a specific time interval.

Tangential acceleration aτ is responsible for the change in linear velocity of a body moving in a circle. It occurs when the angular velocity changes over time (there is angular acceleration ε). This acceleration acts along the tangent to the trajectory.