How Do You Calculate the Speed of a Stone in a Sling?

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SUMMARY

The speed of a stone in a sling can be calculated using the formula V_t = r × ω, where V_t is the tangential speed, r is the radius of the sling, and ω is the angular velocity in radians per second. For a sling length of 0.750 m rotating at 10.0 revolutions per second, the speed is 47.1 m/s. For a sling length of 1.050 m rotating at 8.00 revolutions per second, the speed is 53.1 m/s. The calculations involve determining the circumference of the sling and multiplying it by the rate of rotation.

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  • Understanding of angular velocity and its relationship to linear speed
  • Familiarity with the formula V_t = r × ω
  • Basic knowledge of circular motion concepts
  • Ability to convert revolutions per second to radians per second
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Homework Statement



Young David who slew Goliath experimented with slings before tackling the giant. He found that he could revolve a sling of length 0.750 m at the rate of 10.0 rev/s. If he increased the length to 1.050 m, he could revolve the sling only 8.00 times per second.



What is the speed of the stone for each rate of rotation?

a) ... m/s at 10.0 rev/s

b) ... m/s at 8.00 rev/s

The Attempt at a Solution



I can probably figure this out but I forgot my book and don't want to guess. Please could you tell me the equation that I use.

Thanks.
 
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It is most likely the relationship between angular movement and tangential.
[tex]V_t=r \cdot\omega[/tex]

Casey
 
Thanks, I got it.

I just took the circumference and multiplied that by the rotations/sec.
 

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