Suppose NASA is designing a new spacecraft and they want your help to determine

Question

Suppose NASA is designing a new spacecraft and they want your help to determine the moment of inertia about different rotation axes. They give you a scale model of the spacecraft that is exactly 100 times smaller than the real thing in each dimension. Describe the experiments and calculations you would perform to give NASA the information they need.

The mass of the model will be 100^3 times smaller than the spacecraft's mass, and the moment of inertai of the model will be 100^5 times smaller than the spacecraft's moment of inertia. Why?

Explanation / Answer

experiment needed to be done:

as we know, torque=moment of inertia*angular veloicty

so you can make the model rotate along the axis determined by NASA and calculate torque and angular velocity.

A torque sensor can be used for measuring the torque.

take 10-20 readings for each calculation to reduce the human error and instrument error.

Q2.

as the dimension is reduced by 100 times,

each of length, width and height will reduce 100 times each.

then volume will reduce 100^3 times

as mass=volume*density

and density remains constant

hence as volume decreases 100^3 times, mass will decrease 100^3 times

similarly, moment of inerta=mass*distance from axis through center of mass^2

then as dimension is reduced 100 times, moment of inertia will be reduced by 100^3*100^2=100^5 times.

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