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Question

The restaurant at the top of a very tall building in Seattle rotates 1.08 revolutions every hour. Bria sits 18.2 meters from the center of the restaurant near a window.

a) Through how many radians does Bria turn in 110 minutes? (exact answer)

b)How far does Bria move in 110 minutes? (exact answer)

Answer 1

a) For this problem, we first need to convert our units of revolutions/hour to radians/minute. To do so we need to know that that are 2pi radians in every revolution and 60min in a hour.

1.08 rev x 1 hour x 2pi rad

1 hour 60 min 1 rev

Canceling units and multiplying across we get:

1.08 rev x 1 hour x 2pi rad = 0.036pi rad

1 hour 60 min 1 rev min

Multiplying this rate by the 110 minutes given givens the total radians Bria turned during that time:

0.036pi rad x 110 min = 3.96pi radians

min

b) For this part, we need to know the circumference of the circle Bria is turning. To find this, we can take the 18.2 meters as the radius:

c = 2pi r = (2)(pi)(18.2m) = 36.4pi meters

We can then multiply by the total number of times she traveled around the circle, the 1.08 revolutions:

1.08 x 36.4pi m = 39.312pi meters

Answer 2

Use a series of ratios to find:

a) ( 1.08 Rev/hr )( 1 hr/60min )( 110min )( 2pi radian/Rev ) = XXX radians

and

b) (1.08 Rev/hr )( 1 hr/60min )( 110 min )( 2pi R m / Rev) = YYY m

where R = 18.2 m