In Example 12.3 "A rotating widget", suppose the triangular wedge was taken off the axle and tossed up in the air so that it’s rotating. About what point would the triangular wedge rotate?

Question

BlackTom AI · Accepted Answer

The question asks about the rotational center for a triangular wedge that has been detached and is rotating while tossed in the air, within the context of Example 12.3 'A rotating widget'.
Option 1: 'About a point that lies within the widget, in the area bounded by the plastic rods' — This option suggests the wedge would rotate about some internal point of the widget, which is consistent with rigid-body rotation where every part shares a common instantaneous center of rotation if there is no external torque causing rotation about a different axis. In many textbook setups, an object rotating as a rigid body about an internal axis corresponds to a point inside the body that acts as a instantaneous center of rotation depending on how it’s constrained by the surrounding structure (the plastic rods here). This is a plausible description for the rotation behavior of the wedge when it’s not constrained to an external pivot.

Option 2: 'About a point that lies on one of the plastic rods' — If rotation were about a fixed point on a rod, that would imply the rod itself is acting as a hinge or pivot for the wedge, which is not indicated by the wedge being detached and simply rotating in space. A rotation about a point on the rod would require the wedge to be kinematically tied to that rod in a way that fixes the pivot location to the rod itself, which doesn’t align with the wedge being free to rotate independently in the air.

Option 3: 'About the 300 g mass' — Referencing a mass within the widget as the rotation center would be incorrect in a rigid-body rotation context unless that mass is truly a fixed pivot point. In the typical rotating-widget scenario, the center of rotation is determined by the geometry and constraints of the entire assembly, not by the mass value of a component acting as a pivot. Using a mass as the rotation center conflates inertial properties with kinematic pivot points, which is inaccurate for this setup.

Option 4: 'About the 150 g mass' — Similar to Option 3, selecting a specific mass as the center of rotation misidentifies the true instantaneous center. The mass values influence moments of inertia and dynamics, but the rotation center is a geometric/kinematic point, not a mass tag, unless that mass coincides with a fixed pivot. Without such a fixed pivot, designating a mass as the center would be incorrect.

Option 5: 'About the 250 g mass' — This repeats the same conceptual error as Options 3 and 4, attributing the center of rotation to a particular lumped mass rather than to a physical pivot or an internal instantaneous center determined by the widget’s geometry and constraints. In standard treatments of rotating parts, mass labels do not define the rotation center unless they are physically at a hinge or pivot location.

Putting the reasoning together, the most defensible description among the choices is the one that locates the instantaneous center of rotation inside the widget, in the region bounded by the plastic rods, since it reflects a plausible internal pivot for a freely rotating component within the constrained widget geometry. The other options rely on pivots at a rod, or on individual mass values, which do not capture the actual rotational geometry described in the example.

In Example 12.3 "A rotating widget", suppose the triangular wedge was taken off the axle and tossed up in the air so that it’s rotating. About what point would the triangular wedge rotate?单项选择题

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