Rock whirling in vertical circle

AI Thread Summary
To achieve tangential and radial acceleration equality for a rock whirling in a vertical circle at a 37-degree angle, the required speed can be derived from the equation v² = gr.sin(θ), where g is the acceleration due to gravity (9.8 m/s²) and r is the radius (8 m). The discussion emphasizes the relationship between weight (W), mass (m), and acceleration in the context of circular motion. The equation Wsin(θ) = ma is referenced to establish the connection between forces acting on the rock. Ultimately, the calculations confirm that the speed must satisfy the derived formula for the specific angle. Understanding these dynamics is crucial for analyzing circular motion in physics.
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a rock whirls in a vertical circle of radius 8m. acceleration of gravity 9.8m/s^2

what must the speed be to have tangential=radial acceleration when the string makes a 37 angle with respect to the vertical?

is it Wsinangel=ma

v=Wsinangle*r/m)^1/2 ?
 
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If W is mg, then yes.

v² = gr.sin@
 

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