To find: The angular speed of the wheel in revolutions per minute.
Answer to Problem 111AYU
The angular speed of the wheel in revolutions per minute is 31.47 rev/min .
Explanation of Solution
Given information:
The speed of the cable is 9.55 miles/h and the diameter of the wheel is 8.5 ft .
Concept used:
An object moves around a circular path of radius r at a constant speed .If s is the distance travelled in time t around this circles, then the linear speed v of the object is defined as,
v=st
The angular speed ω of this object is the angle θ (measures in radians ) swept out divided by the elapsed time t that is
ω=θt
The relation between linear speed and angular speed;
v=rω
Here, ω is measured in radius per unit time.
The angular speed of the wheel is calculated as,
v=rωω=vrω=9.55 miles/h|1 miles/min60 miles/h|8.5 ft2|1 mile5280 ft|ω=197.74 rad/min|1 rev/min2π rad/min|
Simplify further,
ω=31.47 rev/min
Thus, the angular speed of the wheel in revolutions per minute is 31.47 rev/min .
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Precalculus
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