Calculate energy-equivalent mass for an ideal rolling shape, or tangential force for a point mass from mass, radius, and angular acceleration.

Ideal rolling without slipping; the shape radius equals the rolling radius. This is an energy-equivalent mass, not actual weight.

Rotational Weight Formula

The point-mass mode calculates tangential force needed to produce angular acceleration ฮฑ at a fixed radius r. This is not gravitational weight or a general distributed-body force formula. 

RW = m ร— r ร— ฮฑ

Variables:

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

To calculate this value, multiply the mass, radius, and angular acceleration together (since tangential acceleration is at = rฮฑ and tangential force is Ft = m at).

The rolling mode uses energy-equivalent mass m + I/rยฒ = m(1 + ฮบ), including translation and rotation. It assumes ideal rolling without slipping and equal rolling and shape radii: ฮบ is 1 for a thin ring, 1/2 for a solid disc, and 2/5 for a solid sphere. This does not change actual mass or gravitational weight.

How to Calculate Rotational Weight?

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

Example Problem #1

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

RW = m*r*ฮฑ

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 = 378 (N)