Question

the tip of a pinwheel is 0.24 m from the center. The pinwheel spins 5 times each second. What is the tangential speed of the tip of the pinwheel?

Answer 1

Answer: 7.539 m/s

Explanation:

The tangential velocity $V$ is defined as the angular velocity $\omega$ by the radius $r$ of the circular motion:

$V=\omega. r$  (1)

Its name is due to the fact that this linear velocity vector is always tangent to the trajectory and is the distance traveled by a body or object in a circular movement in a period of time.

In this sense, $\omega=\frac{2 \pi}{T}$  is the angular velocity, which is inversely proportional to the period $T$ of the circular motion. So equation (1) is expressed as:

$V=\frac{2 \pi}{T}r$  (2)

We already know $r=0.24 m$ , and we can find $T$, knowing the frequency $f$:

$f=5 times/s=\frac{1}{T}$

Isolating $T$:

$T=\frac{1}{f}=\frac{1}{5 times/s}$

$T=0.2 s$ (3)

Substituting (3) in (2):

$V=\frac{2 \pi}{0.2 s}(0.24 m)$  (4)

$V=7.539 m/s$ This is the tangential speed of the tip of the pinwheel

Answer 2

Answer:

D. 7.5

Explanation:

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