- #1

AlanWWW

- 6

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## Homework Statement

A circular plate with radius 0.5 m and mass 5 kg is hung on the wall, fixed at a point that is 0.3 m above its center. The plate can freely rotate about the fixed point with no friction. A very short-duration impulse of 5 N sec, along a direction that is tangential to the circumference of the circular plate, is applied at the bottom point of the plate. From energy conservation, what is the maximum angle of rotation (away from the equilibrium position) attained by the plate?

r = 0.5 m

m = 5 kg

Impulse = 5 Ns

## Homework Equations

w is omega

r is the radius

Moment of Inertia = I_cm + MR^2

Rotational energy = 0.5*I*w^2

angular momentum = linear momentum*r

angular momentum = I*w (if symmetry)

## The Attempt at a Solution

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First, find the moment of inertia by I = I_cm + MR^2

I = 0.5*m*r^2 + m*r^2

= (0.5)(5)(0.5^2)+(5)(0.3^2)

= 1.075Then, find the initial angular velocity

By impulse = Δangular momentum

(I stuck here because the equation" angular momentum = I*w " cannot be used

as it only works when the rotation axis is symmetry)Then the question said from conservation of energy, so it should relate to:

Initial Energy = Final Energy

Initial Energy = E_rotational + E_transitional

(Energy of transitional should not be zero as the center of mass is moving,

I am not sure it is correct or not.)

Final Energy = m*g*h

(However I don't how this equation apply to a rigid body but not a point mass)