What is the relationship between force and weight in rotating a disk?

[mather]

hello

there is a stick fixed in the center of a disk, so that when the stick rotates, it makes the disk rotate too (something like the car wheels), like this:

[PLAIN]https://p.secure.hostingprod.com/@images.boomerangs.com/images/gyroscope.jpg

how can we calculate the relationship between force needed to rotate the disk and the weight of the disk ?

the rotational inertia of the disk resists the torque applied to rotate it

for example if we increase the weight of the disk by 10 lb (from 40 lb to 50 lb), the force needed to maintain a specific rotating speed would increase, but how much exactly?

thanks

 

[tiny-tim]

hello mather!

… how can we calculate the relationship between force needed to rotate the disk and the weight of the disk ?
…
for example if we increase the weight of the disk by 10 lb (from 40 lb to 50 lb), the force needed to maintain a specific rotating speed would increase, but how much exactly?

If the mass is m, the angular velocity is ω, and the moment of inertia is I,

then the rotational equivalent to F = ma is τ = Iω, where τ is the torque of the force (τ = F.d where d is the vector from the axis to the line of application of F).

If you multiply the mass by a factor k (but keep the density constant), then I is also multiplied by k, so you would need to multiply the force by k also.