An object is traveling on a circle with a radius of 6 feet. If in 80 seconds a central angle of 9/4 radians is swept out, then find both t

Question

An object is traveling on a circle with a radius of 6 feet. If in 80 seconds a central angle of 9/4 radians is swept out, then find both the angular speed and the linear speed of the object. Give exact answers. DO NOT provide a decimal approximation.

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Thiên Thanh 4 years 2021-07-30T20:25:59+00:00 1 Answers 17 views 0

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  1. diemkieu
    0
    2021-07-30T20:27:52+00:00
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    Answer:

    The angular speed of the object is 0.0281 rad/s

    The linear speed of the object is 0.169 ft/s

    Explanation:

    Given;

    radius of the circle, r = 6 ft

    time of motion of the object around the circle, t = 80 s

    central angle formed by the object during the motion, θ = 9/4 rad = 2.25 rad

    The angular speed of the object is calculated as;

    \omega = \frac{\theta }{t} = \frac{2.25 \ rad}{80 \ s} = 0.0281 \ rad/s

    The linear speed of the object is calculated as;

    v = ωr

    v = 0.0281 rad/s   x    6ft

    v = 0.169 ft/s

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