As you approach the I-90 exit in your uncle's little red sports car convertible, you happen to notice a cat crossing the road. Not that you have any particular love of cats (especially this one, whose snooty disposition seems to beckon for a game of chicken), but you swerve out of the way, spilling scalding hot coffee all over your new summer duds.
Unknown to you at the time, the auto mechanic, having had a late night out and consequently being somewhat in a fog, forgot to fasten the lug nuts on one of your uncle's tires.
Given your velocity on the exit ramp as 3.2 m/s, a tire mass of 12 kg and radius 29 cm;
a) What is the angular momentum L of uncle's tire immediately upon its departure from its axle (assume the tire is a solid cylinder) in kg m2/s?
I solved this to get 5.57 kg m2/s.
b) Next the tire cruises up an embankment at an angle θ = 27° above the horizontal for 1 meter before launching across Piranha Lake. What is the velocity vfinal of the tire at the top of the embankment in m/s?
For this part I'm having trouble expressing my total kinetic energy (that I solved for) in terms of velocity.
I plugged in the numbers for the initial KE: (1/2)*I*ω2 + (1/2)*m*v2. where I got 92.16 J.
Final KE = Initial KE - m*g*h where h = 1m * sinθ.
My final KE came out to be 38.7707 J.
How do I use this to find the final velocity?