How to Calculate Angular Displacement

You can solve for angular displacement with equations similar to those used for linear displacement. What you’d need is an initial angular velocity and for the angular acceleration to be constant, analogous to the requirement in projectile motion calculations seen in first-semester physics class. The relevant equation is ?(t) = ?(0) + ?(0)xt + 0.5x?xt^2, where ?(t) is the angular displacement after time t has passed, ?(0) is the initial angular velocity value, and ? is the constant angular acceleration. A constant angular acceleration indicates a constant torque is being applied to the object being angularly displaced. ?(t)-?(0) is the angular displacement.

Instructions

1. Suppose you are given that the torque applied to an object of mass weighing 2kg is 4 Newton-meters with mass centered 2m out from the center of rotation. Torque is (tangential force)x(radius of rotation), and tangential force equals mass x acceleration = mass x (radius of rotation x ?). Therefore in this case, dividing out the mass once and the radius twice gives ?=0.5 radians per second-squared.

2. Suppose that the initial angular velocity is 2 radians per second. Suppose further that you want to know the angular displacement after one minute. Then use the formula presented in the introduction to solve for the angular displacement ?(t)-?(0) to get ?(0)xt + 0.5x?xt^2 = 2x60 + 0.5x0.5x60^2 = 1,020 radians.

3. Solve for the displacement in terms of revolutions by dividing by 2?. Continuing with the above example, 1,020 radians/2? = 162.34 revolutions.

References

• "Fundamentals of Physics"; David Halliday and Robert Resnick; 1991
• U. of Guelph: Torque and Angular Acceleration
• Ball State U.: Table Comparing Angular and Linear Motion Equations