1. ans: 3.2 rad/s²; t = Ia

2. ans: 0.88 kg-m²/s; DL = tDt

3. ans: 11 J; KE=.5Iw², w = aDt

4. ans: 4.1 m/s; PE(top)=total KE(bottom); mgh = .5mv²+.5*.4mv²
notice conversion of angular to linear quantities in the last term.

5. ans: 0.42; L=Iw =constant

6. ans: 6.5 m/s²; Use 2 equations:
1: Newton #2: mg-T = ma (gravity - tension = m*net.acceleration),
2: t = rT = Ia = 0.5mr²a = 0.5mra
divide #2 by r to get T and substitute for T in #1.

7. ans: 27 m
Remember centripetal a = v²/r = w²r.
Also have L = Iw = mr²w = constant,
so r²w = L/m = constant = 100*100*0.1 = 1000 (initial values).
Solve for w = 1000/r².
Now go back to centripetal a = w²r = 1x10⁶/r³, = 49.
Finally, r = cuberoot (1x10⁶/49).