A rigid system consists of four point masses connected by negligibly light rods on a…

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

A rigid system consists of four point masses connected by negligibly light rods on a frictionless, horizontal platform. Two masses of

0.40\,\text{kg}

are located at

(+0.20\,\text{m},0)

and

(-0.20\,\text{m},0)

. Two masses of

0.30\,\text{kg}

are located at

(0,+0.15\,\text{m})

and

(0,-0.25\,\text{m})

. All coordinates are in meters, and the

z

-axis is vertical. An engineer wants to spin the system about a vertical axis that passes through the point

P

(+0.05\,\text{m},0)

rather than through the origin. (a) Calculate the rotational inertia of the system about a vertical axis through the origin. Show all steps and include units. (b) Using point

P

as the new axis, compute the rotational inertia of the same mass configuration. Clearly indicate how you determined the required distances. (c) The engineer proposes moving every mass

0.05\,\text{m}

directly toward the origin along a straight radial line from the origin to each mass’s initial position. Determine the new rotational inertia about the axis through point

P

after this shift. (d) Explain in physical terms why moving the masses closer to the axis reduces the energy required to bring the system up to a given angular speed.

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