Kinetics of Rigid Bodies: Force and Acceleration - Theory & Concepts - Mass Moment Of Inertia

Application of Newton's Second Law and Euler's Equations to determine the general plane motion of rigid bodies.

Mass Moment of Inertia & Parallel Axis Theorem

Body Shape

Mass (m)8.0 kg

Radius (R)1.00 m

Torque (

\tau

)3.0 N·m

Centroidal Moment of Inertia:

I_G = \frac{1}{2} m R^2 = 0.5 \times 8 \times 1^2 = 4.000\text{ kg}\cdot\text{m}^2

Parallel Axis Translation:

I_O = I_G + m d^2

I_O = 4.000 + (8)(0.63)^2 = 7.125\text{ kg}\cdot\text{m}^2

Separation d:0.63 m

Ang. Acceleration α:0.42 rad/s²

Spin Speed ω:0.0 rad/s

💡 Drag Axis O to translate the axis of rotation.

G (Centroid / Center of Mass)

O (Axis of Rotation / Pivot)

Distance d between G and O

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