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A disk with a radius of 0.1 m is spinning about its center with a constant angular speed of 10 rad/sec. What are the speed and magnitude of the acceleration of a bug clinging to the rim of the disk?

1) 10 m/s and 10 m/s
2

2) 10 m/s and 0 m/s
2
(Disk spins at constant speed)

3) 0.1 m/s and 1 m/s
2

4) 1 m/s and 10 m/s
2

Respuesta :

xero099

Answer:

[tex]v = 1 \frac{m}{s}, a = 10 \frac{m}{s^{2}}[/tex] (Option 4)

Explanation:

Since the disk is spinning at constant speed, it is noticed that bug is experimenting a speed in tangential direction and acceleration in radial direction. That is to say:

[tex]v = \omega \cdot r\\a = \omega^{2} \cdot r[/tex]

[tex]v = (10 \frac{rad}{s}) \cdot (0.1 m)\\v = 1 \frac{m}{s}[/tex]

[tex]a = (10 \frac{rad}{s} )^{2}\cdot(0.1 m)\\a = 10 \frac{m}{s^{2}}[/tex]

The correct answer is Option 4.

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