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If you are spinning an object using a mass-less string with constant speed in a vertical circle, and when the object is at an angle with the vertical, what happens to the component of weight in the tangential direction?

$$mg \cos\theta + T = \frac{mv^2}{R}$$ $$mg \sin\theta =\ ?$$

or am I completely wrong in assuming no tangential acceleration?

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  • $\begingroup$ It'd be cool if it was a massless spring instead :) $\endgroup$ – Physics Llama Sep 27 '14 at 3:13
  • $\begingroup$ Can you clarify what you're asking? Assuming by constant velocity you mean constant angular velocity then the torque you need to maintain the constant angular velocity changes throughout the rotation because the tangential component of the weight changes throughout the rotation. $\endgroup$ – John Rennie Sep 27 '14 at 6:04
  • $\begingroup$ It has constant speed, I am not talking about angular velocity. I am saying that it has constant speed ( speed is always tangential during circular motion). $\endgroup$ – Ashwin Sep 27 '14 at 11:27
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Imagine what happens when the spring in horizontal. Gravity is pulling down on the mass with no counterforce upwards. Therefore, the whirling mass has to be accelerating downwards.

It's impossible to have vertical circular motion at constant speed with gravity and a purely centripetal force.

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