You place 3 stickers on a globe of the Earth to mark possible vacation destinati

Question

You place 3 stickers on a globe of the Earth to mark possible vacation destinations. The globe has a diameter of 30.5 cm. You place Sticker 1 on Maui (Latitude 21 degrees N, Longitude 156 degrees W), Sticker 2 on London (Latitude 52 N, Longitude 0), and Sticker 3 on Auckland (Latitude 37 S, Longitude 175 E). The globe is sitting with Maui facing you directly. You spin the globe counter-clockwise, with an angular speed of 5.8 rad/s, deciding that the vacation destination that ends up closest to you is the one you will visit this year. The globe comes to a stop 6.2 seconds later.

a) What was the angular acceleration of Sticker 1?

b) What was the angular acceleration of Sticker 2?

c) What was the angular acceleration of Sticker 3?

d) What was the magnitude of the tangential acceleration of Sticker 1?

e) What was the magnitude of the tangential acceleration of Sticker 2?

f) What was the magnitude of the tangential acceleration of Sticker 3?

g) Which vacation destination will you be visiting this year? How many radians away from being directly in front of you is this destination?

Explanation / Answer

Maui distance from axis of rotation d1=rcos21=0.93r=0.14 m

London distance from axis of rotation d2=rcos52=0.62r=0.095 m

Auckland distance from axis of rotation d3=rcos37=0.80r=0.12 m

A)

all stickers have the same angular acceleration ?=d?/dt=5.8/6.2=0.94 rad/s^2

B)

Maui tangential acceleration is a=?d1=0.13 m/s^2

London tangential acceleration is a=?d2=0.09 m/s^2

Auckland tangential acceleration is a=?d3=0.11 m/s^2

C)

the angular distance traveled by the globe is given by

?=?^2/(2?)

?=17,9 rad

n. of rev.=2.85

when the globe stops it is 0.85*2? rad West of Maui

that is Longitude 306 degree West of Maui

then the Longitude is (306+175)-360=121 East

Auckland is the place closets to this point

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