A gerbil wheel has a radius of 3.2 inches. The gerbil can spin the wheel at a rate of 35 rotations per minute. Find the angular speed

Question

A gerbil wheel has a radius of 3.2 inches. The gerbil can spin the wheel at a rate of 35 rotations per minute. Find the angular speed of the wheel in degrees per minute and the linear speed of wheel in inches per minute

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Euphemia 3 years 2021-08-08T13:00:06+00:00 1 Answers 12 views 0

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    2021-08-08T13:01:34+00:00

    Given :

    A gerbil wheel has a radius of 3.2 inches. The gerbil can spin the wheel at a rate of 35 rotations per minute.

    To Find :

    The angular speed of the wheel in degrees per minute and the linear speed of wheel in inches per minute.

    Solution :

    Angular speed is given by :

    \omega = 25\ rpm \\\\\omega = 25\times 360^o \ per \ minute\\\\\omega = 9000^o \ per \  minute

    Now, velocity is given by :

    v = Radius\times \dfrac{RPM}{60\ sec/min}\times 2\pi\ rad/rev\\\\v = 3.2 \times \dfrac{35}{60}\times 2\pi\\\\v = 11.73\ m/s

    Hence, this is the required solution.

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