Find the moments of inertia ix, iy, i0 for a lamina that occupies the part of the disk x2 + y2 ≤ 36 in the first quadrant if the density at any point is proportional to the square of its distance from the origin. (assume that the coefficient of proportionality is k.)

(2) (a) you have a simple circuit that consists of only a battery (δvbat=1.5v) and two resistors with resistance r1=10ω and r2=5ω, connected in series with each other. what is the current running through the battery? (b) you re-arrange your circuit so now r2 is attached in parallel to r1 rather than in series. what is the current running through the battery? (c) you add an additional resistor r3=7ω on the same branch as r2. what is the current running through the battery? (d) what is the power dissipated in r3?

Lacie kicks a football from ground level at a velocity of 13.9 m/s and at an angle of 25.0° to the ground. how long will the ball be in the air before it lands? how far will the football travel before it lands?

When the displacement of a mass on a spring is 12a the half of the amplitude, what fraction of the mechanical energy is kinetic energy? at what displacement, as a fraction of a, is the mechanical energy half kinetic and half potential?