Question

Two masses m are attached to a shaft and a mass M by rods (of negligible mass) each of length l (as illustrated).*


The top two rods are fixed to the shaft, and the bottom two rods are fixed to mass M. As the shaft spins, masses m spin with it and mass M spins about it (it is free to slide along the shaft). If mass M slides up, the angle between the rods and the shaft increases (the rods are hinged at the masses m and M so that the angle can change). When the masses are not spinning, the rods make an angle of 45º with the shaft. Now, the masses are set spinning, with increasing angular velocity ω. What is the least value of ω for which mass M starts to rise?

Answer 1

Answer:

Explanation:                       Two masses m are attached to a shaft and a mass M by rods (of negligible mass) each of length l (as illustrated).*

The top two rods are fixed to the shaft, and the bottom two rods are fixed to mass M. As the shaft spins, masses m spin with it and mass M spins about it (it is free to slide along the shaft). If mass M slides up, the angle between the rods and the shaft increases (the rods are hinged at the masses m and M so that the angle can change). When the masses are not spinning, the rods make an angle of 45º with the shaft. Now, the masses are set spinning, with increasing angular velocity ω. What is the least value of ω for which mass M starts to rise?