- #1

Very_Unwise

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- Homework Statement
- A thin rod with length L and mass M pivoted at one end falls (rotates) frictionlessly from a position parallell to the horisontal, starting from rest. At the moment the rod is completely vertical, it collides with a snowball laying on ice with mass=1/9 M. The snowball sticks on to the rod at the tip of the rod. What is the angular velocity of the combined object (rod+snowball) immediatly after collision?

- Relevant Equations
- Ep = M*g*h

I = 1/3 * M*L^2

Ek= 1/2*I *w^2

P = m*r*v

Assuming no friction anywhere, no drag and perfect inelastic collision

Using conservation of mechanical energy i can determine the rotational speed of the rod right before collision occurs.

mgh=1/2*i*w^2

center of mass falls 1/2*L so we have:

M*g*1/2*L = 1/2*(1/3*M*L^2)*w^2

Solving for w gives w^2=(3*g)/L , g=9.81

w=sqrt (29.43/L)

Using conservation of angular momentum P before = P after collision

m*r*v = m*r*v , v=w*r , r=L

M*w before collision *L^2 = (M+1/9*M)*w*L^2 after collision, divide by L^2

M*sqrt (29.43/L) = 10/9*M *w after collision

solving for w after collision gives

w= 4.88/L

Is this the correct way to do it? I don't think i can use conservation of rotational kinetic energy as the collision is inelastic, not elastic.

I also have P =I * w but i don't see a use for it

Using conservation of mechanical energy i can determine the rotational speed of the rod right before collision occurs.

mgh=1/2*i*w^2

center of mass falls 1/2*L so we have:

M*g*1/2*L = 1/2*(1/3*M*L^2)*w^2

Solving for w gives w^2=(3*g)/L , g=9.81

w=sqrt (29.43/L)

Using conservation of angular momentum P before = P after collision

m*r*v = m*r*v , v=w*r , r=L

M*w before collision *L^2 = (M+1/9*M)*w*L^2 after collision, divide by L^2

M*sqrt (29.43/L) = 10/9*M *w after collision

solving for w after collision gives

w= 4.88/L

Is this the correct way to do it? I don't think i can use conservation of rotational kinetic energy as the collision is inelastic, not elastic.

I also have P =I * w but i don't see a use for it