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Ladybugs on a Rotating Disk

Two ladybugs sit on a rotating disk, as shown in the figure (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?

=> the same as the angular speed of ladybug 2

B) What is the ratio of the linear speed of ladybug 2 to that of ladybug 1?

=> 2

 

C) What is the ratio of the magnitude of the radial acceleration of ladybug 2 to that of ladybug 1?

=> a2/a1 =2

D) What is the direction of the vector representing the angular velocity of ladybug 2? See the figure for the directions of the coordinate axes.

=> 

E) Now assume that at the moment pictured in the figure, the disk is rotating but slowing down. Each ladybug remains “stuck” in its position on the disk. What is the direction of the tangential component of the acceleration (i.e., acceleration tangent to the trajectory) of ladybug 2?

=> 

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