A) A wheel is rotating at 5 radians/sec, and the wheel has a 83-inch diameter. To the nearest foot, what is the speed of a point on the rim in ft/min? B) A pulley of radius 25 cm rotates 7 times in 4 sec. Find the angular speed of the pulley C) A wheel is rotating at 4 radians per sec, and the wheel has a 96-inch diameter. To the nearest foot per minute, what is the speed of a point on the rim? D) The radius of the tires of a car is 18 inches, and they are revolving at the rate of 651 revolutions per minute. How fast is the car traveling in miles per hour? E) Find v for the tip of the hour hand of a clock, if the hand is 7 cm long

Question
Asked Sep 26, 2019
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A) A wheel is rotating at 5 radians/sec, and the wheel has a 83-inch diameter. To the nearest foot, what is the speed of a point on the rim in ft/min?
 
B) A pulley of radius 25 cm rotates 7 times in 4 sec. Find the angular speed of the pulley
 
C) A wheel is rotating at 4 radians per sec, and the wheel has a 96-inch diameter. To the nearest foot per minute, what is the speed of a point on the rim?
 
D) The radius of the tires of a car is 18 inches, and they are revolving at the rate of 651 revolutions per minute. How fast is the car traveling in miles per hour?
 
E) Find v for the tip of the hour hand of a clock, if the hand is 7 cm long
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Expert Answer

Step 1

Let v be the speed of a point on the rim, w be the angular velocity, and r be the radius of the wheel.

Write the given values of the question.

= 5 rad/s
= (5 rad/s)
60 min
=0.0833 rad/1min
d 83 inch
-41.5 inch
2
1 ft
= (41.5 inch)12 inch
= 3.458 ft
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Image Transcriptionclose

= 5 rad/s = (5 rad/s) 60 min =0.0833 rad/1min d 83 inch -41.5 inch 2 1 ft = (41.5 inch)12 inch = 3.458 ft

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Step 2

Write the expression for velocity in terms of radius and ...

V = ro
=(3.458 ft)(0.0833 rad/min
=0.288 ft/min
0.3 ft/min
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Image Transcriptionclose

V = ro =(3.458 ft)(0.0833 rad/min =0.288 ft/min 0.3 ft/min

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