Asolid disk has a total kinetic energy k. what is its rotational kinetic energy krot if it's rolling without slipping? express your answer in terms of the variable k.

the total energy is the sum of the linear and rotational energy: 
K = K_rot + K_lin 

first, we find the rotational kinetic energy of a rotating disc with an angular velocity of w. see the references for the moment of inertia of a disc. 
K_rot = (1/2)(I)(w^2) 
I = (1/2)(m)(r^2) 
K_rot = (1/4)(m)(r^2)(w^2) 

next, we find the linear kinetic energy of a rolling disc: 
K_lin = (1/2)(m)(v^2) 
v = angular velocity * circumference 
= w * (pi * 2 * r) 
K_lin = (1/2)(m)(w*2*pi*r)^2 
= (2*pi^2)(m)(r^2)(w^2) 

we find the total kinetic energy: 
K = K_rot + K_lin 
= (1/4)(m)(r^2)(w^2) + (2*pi^2)(m)(r^2)(w^2) 

and find the rotational contribution: 
K_rot = K * [K_rot/K] 
K_rot = K * [K_rot/(K_rot+K_lin)] 
K_rot = K * (1/4) / [(1/4) + (2*pi^2)] 
K_rot = K / (8*pi^2 + 1)

wavelegth as in spectrum red oygbiv

the following is queen elizabeth’s purposes:

- to encourage the parliament that the technique of picking successors to the seat based merely on birthright needs to be reviewed.

- (not) to convince the parliament that her kid should not be measured as a likely choice for heir to the english power.

- to persuade the parliament that merely since she has a child does not assure that the kid will be a capable leader.

- to sway the parliament how shattering it could be if they proceeded discourteously concerning her or her child.