- #1

Jules575

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- TL;DR Summary
- Struggling to reconcile Newton's second law for linear and rotational acceleration. How are these related for wheels accelerating (linear) a vehicle?

I'm struggling to understand something basic here. If I have a just a wheel, with mass 10kg, and radius 0.25m, and I specify that the CG is accelerating linearly at 1ms

T = 10×0.25 = 2.5Nm

α = T/I where I = 0.5×10kg×(0.25m)

α = 2.5/0.3125 = 8 rads

and lastly, the linear acceleration of the CG of the wheel is given by

a = α×r = 8×0.25 = 2ms

This is double what I needed, why does using the force from Newton's second law for linear motion not agree with the law for rotational motion?

Any help greatly appreciated!

^{-2}, how do I calculate the force needed to do this? Using F = ma gives 10N, but using this value for torque calculation on the wheel givesT = 10×0.25 = 2.5Nm

α = T/I where I = 0.5×10kg×(0.25m)

^{2}= 0.3125 kgm^{2}α = 2.5/0.3125 = 8 rads

^{-2}and lastly, the linear acceleration of the CG of the wheel is given by

a = α×r = 8×0.25 = 2ms

^{-2}This is double what I needed, why does using the force from Newton's second law for linear motion not agree with the law for rotational motion?

Any help greatly appreciated!