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a wheel with a tire mounted on it rotates at a constant rate of 2.89 times a second. A tack is stuck in the tire at a distance 39.1cm from the rotation axis. noting that for every rotation the tack travels one circumference. find the tacks tangential speed.
__________m/s
what is the tacks radial acceleration?
___________m/s^2

Respuesta :

Answer:

(A) Tangential speed will be equal to 7.09 m/sec

(B) Radial acceleration will be equal to [tex]128.5629rad/sec^2[/tex]  

Explanation:

We have given angular speed of the wheel [tex]\omega =2.89rev/sec=2.89\times \frac{2\pi rad}{sec}=18.149rad/sec[/tex]

Radius of the track r = 39.1 cm = 0.391 m

(A) Tangential speed will be equal to [tex]v=\omega r[/tex], here [tex]\omega[/tex] is angular speed and r is radius

So tangential speed [tex]v=18.149\times 0.391=7.09m/sec[/tex]

So tangential speed will be equal to 7.09 m/sec

(B) Radial acceleration will be equal to [tex]a=\frac{v^2}{r}=\frac{7.09^2}{0.391}=128.5629rad/sec^2[/tex]

So radial acceleration will be equal to [tex]128.5629rad/sec^2[/tex]

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