# Ladybugs - Ladybugs on a Rotating Disk Two ladybugs sit on...

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Ladybugs on a Rotating Disk Two ladybugs sit on a rotating disk (the ladybugs are at rest with respect to the surface of the disk and do not slip). Ladybug 1 is halfway between ladybug 2 and the axis of rotation. A. What is the angular speed of ladybug 1? one-half the angular speed of ladybug 2 the same as the angular speed of ladybug 2 two times the angular speed of ladybug 2 one-quarter the angular speed of ladybug 2 B. What is the ratio of the linear speed of ladybug 2 to that of ladybug 1? Answer numerically. 2 C. At the instant shown in the figure, what is the direction of the the radial component of the acceleration of ladybug 2? D. What is the ratio of the radial acceleration of ladybug 2 to that of ladybug 1? Answer numerically. 2 E. What is the direction of the vector representing the angular velocity of ladybug 2? F. In general, velocity is represented by a vector. Let represent the velocity of ladybug 1. Angular velocity is also often represented by a vector, so let that of ladybug 1 be given by . Take to be the vector from the axis of rotation to ladybug 1. Which of the following equations correctly describes the relationship between the velocity , angular velocity , and position of ladybug 1?

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G. Now assume that at the moment pictured in the figure, the disk is rotating but slowing down. What is the direction of the tangential component of the acceleration (i.e. acceleration tangent to the motion) of ladybug 2? [ Print ] Moment of Inertia and Center of Mass for Point Particles Ball A, of mass , is connected to ball B, of mass , by a massless rod of length . The two vertical dashed lines in the figure, one through each ball, represent two different axes of rotation, axes a and b . These axes are parallel to each other and perpendicular to the rod. The moment of inertia of the two-mass system about axis a is , and the moment of inertia of the system about axis b is . It is observed that the ratio of to is equal to 3: Assume that both balls are pointlike; that is, neither has any moment of inertia about its own center of mass. A. Find the ratio of the masses of the two balls. Express your answer numerically. = 1/3 B. Find , the distance from ball A to the system's center of mass. Express your answer in terms of , the length of the rod. = 3*L/4 [ Print ]
Scaling of Moments of Inertia Learning Goal: To understand the concept of moment of inertia and how it depends on mass, radius, and mass distribution. In rigid-body rotational dynamics, the role analogous to the mass of a body (when one is considering translational motion) is played by the body's moment of inertia. For this reason, conceptual understanding of the motion of a rigid body requires some understanding of moments of inertia. This problem should help you develop such an understanding. The moment of inertia of a body about some specified axis is

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## This note was uploaded on 10/22/2009 for the course NBNM nmbn taught by Professor Mn during the Spring '09 term at École Normale Supérieure.

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Ladybugs - Ladybugs on a Rotating Disk Two ladybugs sit on...

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