- #1
ft92
- 19
- 1
Homework Statement
The Attempt at a Solution
A) for disk,[/B]
let w is the angular speed of the disk at the lowest point.
moment of Inertia of disk about pivot, P = 0.5*M*R^2 + M*R^2
= 1.5*M*R^2
Apply conservation of energy
initial potentila energy = finalkinetic energym*g*R = (1/2)*I*w^2
m*g*R = (1/2)*1.5*m*R^2*w^2
m*g*R = (1/2)*1.5*m*(R^2*w^2)
g*R = (1/2)*1.5*v_disk^2
2*g*R = 1.5*v_disk^2
v_disk = sqrt(2*g*R)/sqrt(1.5)
= 0.816*sqrt(2*g*R)
= 0.816*v <<<<<<------Answer (wrong! and i don't know why)B) for hoop,
let w is the angular speed of the hoop at the lowest point.
moment of Inertia of hoop about pivot, P = M*R^2 + M*R^2
= 2*M*R^2
Apply conservation of energy
initial potentila energy = finalkinetic energym*g*R = (1/2)*I*w^2
m*g*R = (1/2)*2*m*R^2*w^2
m*g*R = (1/2)*2*m*(R^2*w^2)
g*R = (1/2)*2*v_hoop^2
2*g*R = 2*v_hoop^2
v_hoop = sqrt(2*g*R)/sqrt(2)
= 0.707*sqrt(2*g*R)
= 0.707*v <<<<<<------Answer ( wrong and i don't know why)