is there an equation with moment of inertia?

Question

there are these two questions that have moment of inertia. for example one of them is:
a bowling ball has a mass of 7kg, a moment of inertia of 2.8*10(-2)kgm(2), and a radius of .10m if it rolls down the lane without slipping at a linear speed of 4m/s, its total kinetic energy is

-the numbers in parentheses are exponents or superscripts. however you call them.

my teacher had given equations but i dont remember him ever giving us an equation with moment of inertia.

if it was KE=1/2 mv(2) then there wouldnt be anywhere to put the radius and i dont know what the symbol for moment of inertia would be.

so basically what im trying to ask is, does anyone know an equation for this type of problem?

Answer 1

The total KE is the sum of the linear and rotational KE.
Mat gave you the equation for rotational, and you seem to know the eqn for linear. He didn't mention that ω, the angular velocity must be expressed in radians/sec, so at a given speed down the lane, ω is v/r. So your final eq is:

KEtot = mv²/2 + I(v/r)²/2

Answer 2

You can think of moment of inertia as a type of mass when dealing with rotating systems.

Rotational kinetic energy is

KE = 1/2 I w^2 where I is the moment of inertia and w is the angular velocity.