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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). (Figure 1) Ladybug 1 is halfway between ladybug 2 and the axis of rotation.

**Part A**, What is the angular speed of ladybug 1?

1, one-half the angular speed of ladybug 2

2, the same as the angular speed of ladybug 2

3, twice the angular speed of ladybug 2

4, one-quarter the angular speed of ladybug 2

**Part B**, What is the ratio of the linear speed of ladybug 2 to that of ladybug 1? Answer numberically.

**Part**

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

Answer numberically.

a

_{2 }⁄ a_{1}=**Part 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.

1, +x

2, -x

3, +y

4, -y

5, +z

6, -z

**Part 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?

1, +x

2, -x

3, +y

4, -y

5, +z

6, -z

♦ Relevant knowledge

The linear speed is influenced by the radius as well as the velocity of an object moving around its direction of its rotation. When you alter either or both of these elements, the linear speed is affected similarly For instance with the same angular velocity with growing distance to the direction of the rotation, the linear speed will increase. To resolve this problem, it is essential to use the notion of linear speed, in conjunction with the required calculations tools.

a) Angular velocity is same for both ladybugs

b) Linear speed ratio = v

_{2}⁄ v_{1}= w r_{2}⁄ w r_{1}= r_{2}⁄ r_{1}= 2 r ⁄ r = 2c) Radial acceleration ratio = w

^{2 }r_{2}⁄ w^{2 }r_{1}= r_{2}⁄ r_{1}= 2d) Direction of angular velocity of bug

_{2}= + ze) Direction of tangential acceleration = – y