Rotational Weight Calculator

Reviewed By: Patrick Myers (BSME)

Enter the mass, the radius, and the angular acceleration into the Rotational Weight Calculator. In this calculator, “rotational weight” refers to the tangential force required to produce an angular acceleration for a point mass at radius r (it is not gravitational weight W = mg). The calculator will evaluate this tangential force.

Pick a scenario, enter your numbers, get the answer.

Wheel / rotating part

From angular acceleration

Mass of the rotating part

Mass distribution

Rotational Weight Formula

The following formula is used to calculate the value labeled “Rotational Weight” in this calculator. Physically, it is the tangential force needed to produce angular acceleration α for a point mass at radius r.

RW = m \cdot r \cdot \alpha

Variables:

RW is the tangential force at radius r (N)
m is the mass (kg)
r is the radius (m)
α is the angular acceleration (rad/s^2)

To calculate this value, multiply the mass, radius, and angular acceleration together (since tangential acceleration is a_t = rα and tangential force is F_t = m a_t).

How to Calculate Rotational Weight?

The following two example problems outline the steps and information needed to calculate the Rotational Weight.

Example Problem #1

First, determine the mass (kg).
- The mass (kg) is calculated to be : 3.
Next, determine the radius (m).
- The radius (m) is measured to be: 4.
Next, determine the angular acceleration (rad/s^2).
- The angular acceleration (rad/s^2) is found to be: 5.
Finally, calculate the Rotational Weight using the formula above:

RW = m*r*α

The values provided above are inserted into the equation below and computed.

RW = 3*4*5 = 60.00 (N)

Example Problem #2

The variables required for this problem are provided below:

mass (kg) = 6

radius (m) = 7

angular acceleration (rad/s^2) = 9

Test your knowledge and check your answer with the calculator.

RW = m*r*a = (N)

Follow-Up Calculations

If a wheel-and-tire upgrade adds about 24 lb of rotational weight at each corner, that is roughly 96 lb of extra effective mass the drivetrain has to spin up. You can use the push needed at the tires to see how that extra rotating mass changes launch force at a given acceleration, which is why lightweight wheels often feel quicker off the line even when the car's curb weight barely changes.

If your truck picks up 15 lb of rotational weight per wheel after a tire-and-wheel change, that's about 60 lb of extra effective load before you even factor in passengers or cargo. A quick check with your hill-climbing limit shows how that extra load can shave a little off the steepest grade the vehicle can hold at the same gearing and torque.

Adding a set of heavier off-road wheels that works out to 18 lb of rotational weight per corner means the suspension is carrying about 72 lb more unsprung mass. If you want to see whether that still matches your setup, use what your suspension must carry to think through how the added wheel weight affects ride quality, bottoming resistance, and spring choice.