Machinery's Handbook Motion with Constant Acceleration
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Description
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:
- v = u + at
- s = ut + 0.5at^2
- v^2 = u^2 + 2as
- 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:
-
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.
-
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.
-
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.
-
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.
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