00:01
Show how to relate the translational velocity to the angular velocity.
00:06
Now, for part a, we have this expression v is equal to r omega.
00:12
V is our translational velocity and omega is our angular velocity.
00:17
So this is the equation we would want to use.
00:20
Now, we'd like to calculate the total kinetic energy.
00:24
To calculate our total kinetic energy, we need to consider both of these kinetic energy components.
00:32
Now, our translational kinetic energy is 1 half mass initial velocity squared.
00:43
K e rotational is 1 half i omega squared.
00:48
Now, for a solid sphere, our moment of inertia is 2 fifths mass radius squared.
00:55
So now we can just calculate our total kinetic energy as 1 half mass initial velocity squared plus 1 half times 2 fifths m radius squared times omega squared.
01:09
So that's our expression.
01:12
Now, we can simplify this if we'd like to as well...