Physics Review Packet, some problems i'm stuck on

[adnama]

Just a few questions from a review packet I'm stuck on, any help would be appreciated!

1) The moment of inertia about its axis is given as .5 mr^2. If this cylinder rolls without slipping the ratio of it's rotational kinetic energy to it's translational kinetic energy is
a. 2:1
b. 1:1
c. 1:2 >My guess<
d. 1:3

I'm assuming Rotational Kinetic Energy = (.5mr^2)(w^2) has something to do with this

2) An object’s angular momentum changes by 20 kg,m2/s in 4.0 s. What magnitude average torque acted on this object?
A. 2.5 N’m >my guess<
B. 5.0 N-m
C. 40 N-m
D. 80 N’m

I'm not sure what equation I'm supposed to use

3) A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What is the angular acceleration of the cylinder?
(It's like a circle inside a circle)
A) 1.0 rad/s2
B) 0.60 rad/s2 >my guess<
C) 0.40 rad/s2
D) 0.80 rad/s2

I did angular acceleration = ((R1F1)-(R2F2))/mr1^2 and the closest i got was to .6

4) A solid sphere of mass 1.0 kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined plane?
A) 3.7 m/s >My guess<
B) 4.4 m/s
C) 5.6 m/s
D) 6.3 m/s

my final equation was gh=(7/10)v^2

5)A railroad car with a mass of 200 kg is going at 10 m/s. A 70 kg stunt man drops directly down on it from a distance of 4 m above. What is the speed of the railroad car after?
a. 4.7 m/s
b. 7.4 m/s >my guess<
c. 2.8 m/s
d. 10 m/s

Totally lost

6) A projectile is launched with an initial velocity of 60 m/s at an agnle of 30 degrees above the horizontal. How far will it go?
a. 318 m
b. 160 m >my guess<
c. 152 m
d. 184 m

I feel like this should be simple, and I'm using 2d kinematics but the answers I get don't match up

 

[zachzach]

1) What is the translational kinetic energy? What is v in terms of w?

2) Similar to Newton's Second Law, \vec{F}_{net} = \frac{d\vec{p}}{dt} , What does \tau_{net} = ?

3) I don't really understand the picture.

4) Right.

5) Conservation of Momentum.

6) Show your work.