Calculating Required Torque for Rotating an Object at 1RPM in 1 Second

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The discussion focuses on calculating the torque required to rotate a 20kg object from 0 to 1 RPM in 1 second using a gear with a diameter of 30mm and a shaft diameter of 10mm. The torque formula used is Torque = Force x Radius, where the radius is 0.005m. The calculations involve determining force through mass and acceleration, with acceleration derived from velocity and time. The final torque equation presented is T = 0.186/t Nm, indicating a dependency on time for the acceleration phase.

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PC22
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Hi I am trying to work out the torque required to rotate an object from 0 to 1RPM in 1 second (1 second accelerate to 1RMP) , its working in time laps so very small movement is required.

The diameter of the gear is 30mm and the diameter of the shaft is 10mm, the object on top weights 20kg it's sitting on a low friction bearing.

So far I have

Torque = F x r

r = radius of the cylinder = 0.005

Force = mass x acceleration
where mass = 20kg

accel = velocity/time

velocity = r x ω (rotational speed)

where ω at 1RPM = 6.28 rad/sec

So v = 0.005 x 6.28 = 0.0314 m/s

Therefore accel = 0.0314/t

Therefore T = 12 x 0.031/t x 0.005
= 0.186/t Nm

I know there is a lot more to this but I am very new to this and out of my comfort zone in terms of engineering knowledge (I'm a product designer) , I've mainly been following pre worked examples I've found online. Would really appreciate some help and guidance.
 
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