A horizontal metallic rod is rotating about a vertical axis through the middle of the rod. The length of the rod is L= 1.2 m, the density rho = 6.9 g/cm3, and the ultimate strength of the metal is Su = 4x10 8 N/m 2. Calculate the maximum angular speed the rod can withstand before breaking (in rad/s).
2007-11-09 18:33:19 · 1 answers · asked by Talal B 1 in Science & Mathematics ➔ Physics
The maximum force will occur at the center of the rod. The centrifugal force increases linearly from center to end (F = m*r*w^2), so the rod can be treated as if all the mass were located at the center of mass of each arm. That mass center is at R/2 = L/4, the mass of each arm is rho*(π/4)•d^2*R The force from each arm is then
F = m*r*w^2 = rho*(π/4)•d^2*R * R/2 *w^2
The stress in the rod is 2F/Ar = 2F / (π/4 * d^2)
T = rho*R^2*w^2
Therefore w = √[T/rho] / R, put in Su for T to get w at breaking point. Since R = L/2,
w = 2√[Su/rho] / L
2007-11-09 19:29:52 · answer #1 · answered by gp4rts 7 · 0⤊ 0⤋