Question

A wheel with radius 41.5 cm rotates 5.13 times every second.

Answer 1

The tangential speed of a wad of chewing gum to the rim of the wheel is approximately 1337.659 centimeters per second.

Let suppose that the wheel rotates at constant angular speed ($\omega$), in radians per second, the tangential speed of a wad of chewing gum to the rim of the wheel ($v$), in centimeters per second, is:

$v = 2\pi\cdot r\cdot f$ (1)

Where:

• $r$ - Radius of the wheel, in centimeters
• $f$ - Frequency, in hertz

If we know that $f = 5.13\,hz$ and $r = 41.5\,cm$, then the tangential speed of the chewing gum is:

$v = 2\pi\cdot (41.5\,cm)\cdot (5.13\,hz)$

$v \approx 1337.659\,\frac{cm}{s}$

The tangential speed of a wad of chewing gum to the rim of the wheel is approximately 1337.659 centimeters per second.

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