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spayn [35]
3 years ago
9

Your 64-cm-diameter car tire is rotating at 3.3 rev/swhen suddenly you press down hard on the accelerator. After traveling 250 m

, the tire's rotation has increased to 6.4 rev/s. What was the tire's angular acceleration? Give your answer in rad/s^2.
Physics
2 answers:
umka21 [38]3 years ago
6 0

Answer:

0.76 rad/s^2

Explanation:

First, we convert the original and final velocity from rev/s to rad/s:

v_o = 3.3\frac{rev}{s} * \frac{2\pi rad}{1rev} =20.73 rad/s

v_f = 6.4\frac{rev}{s} * \frac{2\pi rad}{1rev}=40.21 rad/s

Now, we need to find the number of rads that the tire rotates in the 250m path. We use the arc length formula:

D = x*r \\x = \frac{D}{r} = \frac{250m}{0.64m/2} = 781.25 rads

Now, we just use the formula:

w_f^2-w_o^2=2\alpha*x

\alpha =\frac{w_f^2-w_o^2}{2x} = \frac{(40.21rad/s)^2-(20.73rad/s)^2}{2*781.25rad} = 0.76 rad/s^2

olasank [31]3 years ago
3 0

Explanation:

The given data is as follows.

   Initial velocity, u = 3.3 rev/s \times 2 \pi rad/rev

                           = 20.724 rad/sec

   Final velocity, v = 6.4 rev/s \times 2 \times pi rad/rev    

                           = 40.192 rad/sec

Now, we will calculate the value of angular rotation (d) as follows.

          d = No. of revolutions × 2 \pi rad/rev

         d = (\frac{250 m}{2 \pi r}) \times 2 \pi

            = \frac{250}{0.32}

            = 781.25 rad

Also, we know that,

                v^{2} = u^{2} + 2ad

or,              a = \frac{(v^{2} - u^{2})}{2d}

                      = \frac{(40.192)^{2} - (20.724)^{2})}{2 \times 781.25}

                      = \frac{1615.39 - 429.48}{1562.5}

                     = 0.7589 rad/s^{2}

Thus, we can conclude that the tire's angular acceleration is 0.7589 rad/s^{2}.

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