Rotation of Rigid Objects

A rigid object is one where the distance between any two points remains constant during motion. This allows us to treat the entire system as a single rotating body rather than tracking each particle separately.

Consider two points $A$ and $B$ on an object separated by a distance $L$. For a rigid object, this distance $L$ stays the same at all times during rotation. Because of this, every point on the object shares the same angular displacement $\Delta \theta$, angular velocity $\omega$, and angular acceleration $\alpha$.

When can a system be modeled as rigid?

An object qualifies as a rigid body when there is no bending, stretching, or deformation. Examples include a spinning wheel, a rotating door, or a tumbling textbook. In these cases, all internal distances remain fixed.

When does the rigid model fail?

Systems where relative positions between points change during motion cannot be modeled as rigid. A spinning pizza dough that stretches out or a figure skater moving their arms during a pirouette are examples of non-rigid objects since they change shape during their motion, causing the distances between internal points to vary.

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