Name (print): A ladybug and a gentlemanbug are sitting on a turn table with an a

Question

Name (print): A ladybug and a gentlemanbug are sitting on a turn table with an angular speed of w. The gentlemanbug is 0.25 m from the center and the ladybug is 0.20 m from the center. Who has the greater angular speed and who has the greater linear speed? Explain your answer using the equations. a) Calculate the angular speed for both the gentlemanbug and ladybug if they rotate through 70 degrees in 1.25 seconds. b) c) Calculate the linear speed of each bug. d) Calculate the centripetal acceleration for each bug. e) Calculate the period of rotation for each bug. 10 If the turntable slows to a stop in 3 seconds find the angular acceleration and linear acceleration for each bug.

Explanation / Answer

a)

Angular speed is constant for both of them.

For linear speed, as we know

V= rw

Here v is directly proportional to radius and radius of gentleman bug is greater than lady so it has higher velocity.

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b)

Angular velocity= 70*pi/180/1.25 = 0.977 rad/s

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c) linear speed of gentleman bug= 0.25*0.977= 0.244 m/s

Linear speed of lady bug= 0.2*0.977 = 0.1954 m/s

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d)

Centripital acceleration of gentleman bug=0.244^2/(0.25)= 0.238 m/s^2

Centripital acceleration of lady bug= 0.1954^2/0.2 = 0.191 m/s^2

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e)

w= 2*3.14/T

T= 6.428 second

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f) using first equation of motion

a= - v/t

Acceleration for gentleman bug= 0.244/3= - 0.081 m/s^2

Acceleration of lady bug= - 0.0651 m/s^2

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Commemt in case any doubt.. good luck

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