How to Find Revolutions From Angular Acceleration

How to Find Revolutions From Angular Acceleration
••• Givaga/iStock/GettyImages

The equation of motion for a constant acceleration:

x(t)=x(0)+v(0)t+\frac{1}{2}at^2

has an angular equivalent:

\theta(t)=\theta(0)+\omega(0)t+\frac{1}{2}\alpha t^2

For the uninitiated, θ(t) refers to the measurement of some angle at time ​t​ while θ(0) refers to the angle at time zero. ω(0) refers to the initial angular speed, at time zero. α is the constant angular acceleration.

An example of when you might want to find a revolution count after a certain time ​t​, given a constant angular acceleration, is when a constant torque is applied to a wheel.

    Suppose you want to find the number of revolutions of a wheel after 10 seconds. Suppose also that the torque applied to generate rotation is 0.5 radians per second-squared, and the initial angular velocity was zero.

    Plug these numbers into the formula in the introduction and solve for θ(t). Use θ(0)=0 as the starting point, without loss of generality. Therefore, the equation

    \theta(t)=\theta(0)+\omega(0)t+\frac{1}{2}\alpha t^2

    becomes

    \theta(10)=0+0+\frac{1}{2}\times\frac{1}{2}\times 10^2=25\text{ radians}

    Divide θ(10) by 2π to convert the radians into revolutions. 25 radians / 2π = 39.79 revolutions.

    Multiply by the radius of the wheel, if you also want to determine how far the wheel traveled.

    Tips

    • For nonconstant angular momentum, use calculus to integrate the formula for the angular acceleration twice with respect to time to get an equation for θ(t).

Related Articles

How to Calculate a Change in Momentum
How To: Degree to Radian Conversion
How to Calculate Tangential Force
How to Calculate Tangential Speed
How to Use Newtons to calculate Meters Per Second
How to Find the Inertia of an Object
How to Calculate the Velocity of an Object Dropped...
How to Determine Magnitude of Velocity
How to Calculate Tire Turns Per Mile
How to Calculate the Distance/Speed of a Falling Object
How to Convert Seconds Into Miles Per Hour
How to Find Acceleration in G's
How to Calculate Wheel Circumference
How to Multiply Vectors
The Types of Velocity
How to Find Resultant Displacement in Physics
How to Calculate the Jump Height From Acceleration
How to Compare KTS to MPH in Wind Speed
How to Calculate Holding Torque