PHYS 216 Lab 5

PHYS 216 Lab 5 Recent

Moment of Inertia, Torque, and Rigid Body Rotation

Section A

A spaceship in deep space, initially at rest, is struck by an asteroid. As a model for the ship, consider it to be a thin, rectangular rod,

and assume the collision takes place on the top surface. For an object that’s free to rotate (unconstrained), the axis of rotation is

through the object’s center of mass (CM). Therefore, in this case, the moment of inertia (I) of the ship can be found from

I = (1/12) × M × L2

where M is the mass of the ship and L is the length.

i) Assume the mass of the ship is 40,000 kg. Fill in the table on the right and plot the moment of inertia as a function of the length

of the ship for L = 20, 40, 80, 160, and 320 m.

ii) Assume the length of the ship is 160 m. Fill in the table on the right and plot the moment of inertia as a function of mass

for M = 10k, 20k, 40k, 80k and 160k kilograms.

Question: After the collision, would the spaceship be translating as well as rotating? Explain why or why not.

Moment of Inertia, Torque, and Rigid Body Rotation

Section B

A spaceship in deep space, initially at rest, is struck by an asteroid. As a model for the ship, consider it to be a thin, rectangular rod,

and assume the collision takes place on the top surface. For an object that’s free to rotate (unconstrained), the axis of rotation is

through the object’s center of mass (CM). Therefore, in this case, the moment of inertia (I) of the ship can be found from

I = (1/12) × M × L2

where M is the mass of the ship and L is the length.

The mass of the spaceship is 40,000 kg, its length is 160 m and the force from the asteroid is 20,000 N. The asteroid hits

the ship perpendicular to its top surface and 30 m from it’s center of mass. The collision lasts for 0.01 s.

Determine the following parameters: the torque from the collision (τ), the angular acceleration of the ship during the collision (α),

the angular velocity of the ship after the collision (ω), and the period of the ship’s rotation in seconds and days.

i) Fill in the table on the right and make a plot of the torque as a function of the incident angle if the angle of incidence in degrees

relative to the surface is θ = 90, 80, 40, 20, 10, and 1.

ii) Fill in the table on the right and make a plot of the period (in days) as a function of the incident angle if the angle of incidence

in degrees relative to the surface is θ = 90, 80, 40, 20, 10, and 1.

Question: From the plot, approximately what angle results in the ship having a period of 2 days?