Pre lab physics for engineers PDF

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Pre lab...

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Torail Murphy

Prelab 6 - Rotational Inertia To prepare you for Lab 6, we will analyze how the kinetic energy is related to the moment of inertia in rotational systems..

Background Lab 6 will involve the use of a hanging mass wrapped around a pulley to increase the angular velocity of an object such as the gray horizontal disk indicated below. As it rotates, we can record its displacement and angular velocity to learn about kinetic energy and rotational inertia. Fig.(1)

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1501_PreLab_6.nb

Kinetic Energy of Rotation System 1 As shown in Fig.(2), a small square mass m connected to a massless rod moves in a circle of radius r with constant velocity v. In the following, approximate the square mass m as a point mass. Fig.(2)

Q1

◼ Express the kinetic energy of the square mass in terms of angular velocity ω, r , and m. (Hint: In circular motion, how is ω related to v?)

Km =

1 2

m(ωr)2

Q2

◼ If we express the kinetic energy as K = 21 Iω2, what is I for System 1? I is the moment of inertia. I is equal to the sum of mass * r^2. I = Σm*r^2

System 2 Consider now the configuration below:

1501_PreLab_6.nb

Fig.(3)

Q3

◼ Express the total kinetic energy of System 2 in terms of ω, r , and m.

Km =  12 m(ωr)2 +  21 m(.5 ωr)2 = (5mr^2w^2)/8 Q4

◼ If we express the kinetic energy as K = 21 Iω2, what is I for System 2? I = (5mr^2)/4 Q5

◼ Which mass has a larger kinetic energy, the mass at radius r or the mass at r / 2 ? Why?

Kmr/2 =

1 K 4 mr

The mass with the larger radius (r) is four times greater than that of r/2.

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