Machinery's Handbook Motion with Constant Acceleration

This spreadsheet has dozens of linear and angular motion with constant acceleration equations from Machinery's Handbook 26th edition. It is laid out in a simple to use format and contains a table of contents page with hyperlinks.

Linear Acceleration from Rest

unknown: distance

known: acceleration, time

known: final velocity, time

known: final velocity, acceleration

unknown: final velocity

known: acceleration, time

known: distance, time

known: acceleration, distance

uknown: time

known: distance, final velocity

known: distance, acceleration

known: final velocity, acceleration

unknown: acceleration

known: distance, time

known: distance, velocity

known: final velocity, time

Angular Acceleration from Rest

unknown: angle of rotation

known: angular acceleration, time

known: final angular velocity, time

known: final angular velocity, angular acceleration

unknown: final angular velocity

known: angular acceleration, time

known: angle of rotation, time

known: angular acceleration, ratation angle

unknown: time

known: angle of rotation, angular velocity

known: angle of rotation, angular acceleration

known: angular acceleration, angular velocity

unknown: angular acceleration

known: angle of rotation, time

known: angle of rotation, final angular velocity

known: final angular velocity, time

Linear Acceleration from Initial Velocity

unknown: distance

known: acceleration, time, initial velocity

known: initial velocity, final velocity, time

known: initial velocity, final velocity, acceleration

known: final velocity, acceleration, time

Unknown: Final Velocity

known: initial velocity, acceleration, time

known: initial velocity, distance, time

known: initial velocity, acceleration, distance

known: distance, acceleration, time

unknown: initial velocity

known: final velocity, acceleration, distance

known: final velocity, distance, time

known: final velocity, acceleration, time

known: distance, acceleration, time

unknown: time

known: initial velocity, final velocity, acceleration

known: intial velocity, final velocity, distance

unknown: acceleration

known: initial velocity, final velocity, distance

known: initial velocity, final velocity, time

known: initial velocity, distance, time

known: final velocity, distance, time

Angular Acceleration from Intial Angular Velocity

unknown: angle of rotation

known: acceleration, time, initial velocity

known: initial velocity, final velocity, time

known: intial velocity, final velocity, acceleration

known: intial velocity, final velocity, acceleration

unknown: final angular velocity

known: initial velocity, acceleration, time

known: initial velocity, rotation angle, time

known: initial velocity, acceleration, rotation angle

known: rotation angle, acceleration, time

unknown: initial angular velocity

known: final velocity, acceleration, angle of rotation

known: final velocity, angle of rotation, time

known: final velocity, acceleration, time

known: angle of rotation, acceleration, time

unknown: time

known: initial velocity, final velocity, acceleration

known: initial velocity, final velocity, angle of rotation

unknown: angular acceleration

known: initial velocity, final velocity, angle of rotation

known: initial velocity, final velocity, time

known: initial velocity, angle of rotation, time

known: final velocity, angle of rotation, time

Calculation Reference
Machinery's Handbook

Acceleration and Velocity

Equations of Motion

Constant acceleration motion, also known as uniformly accelerated motion, is a type of motion where an object's velocity changes at a constant rate over time. In other words, the object's acceleration remains constant throughout the motion. This type of motion is often seen in physics problems and real-world scenarios, such as a car accelerating from rest or a freely falling object under the influence of gravity.

There are four main kinematic equations that describe constant acceleration motion:

1. v = u + at
2. s = ut + 0.5at^2
3. v^2 = u^2 + 2as
4. s = 0.5(u + v)t

In these equations:

• 'v' represents the final velocity of the object
• 'u' represents the initial velocity of the object
• 'a' represents the constant acceleration
• 't' represents the time elapsed
• 's' represents the displacement (change in position) of the object

Here's a brief explanation of each equation:

1. v = u + at: This equation relates the initial and final velocities of the object, the constant acceleration, and the time elapsed. It shows that the final velocity is equal to the initial velocity plus the product of acceleration and time.

2. s = ut + 0.5at^2: This equation relates the displacement of the object to its initial velocity, constant acceleration, and time elapsed. It shows that the displacement is equal to the product of the initial velocity and time, plus half of the product of acceleration and the square of time.

3. v^2 = u^2 + 2as: This equation relates the initial and final velocities, constant acceleration, and displacement of the object. It shows that the square of the final velocity is equal to the square of the initial velocity plus twice the product of acceleration and displacement.

4. s = 0.5(u + v)t: This equation relates the displacement, initial and final velocities, and time elapsed for an object in constant acceleration motion. It shows that the displacement is equal to half the sum of the initial and final velocities multiplied by the time elapsed.

These equations are useful for solving various problems related to constant acceleration motion, such as calculating the time it takes for an object to reach a certain velocity, the distance it travels during that time, or the acceleration needed to achieve a specific change in velocity.