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**1. A thin, uniform, metal bar, 2.5 m long and weighing 90 N, is hanging vertically from the ceiling by a frictionless pivot.**Suddenly it is struck 1.3 m below the ceiling by a small 4-kg ball, initially traveling horizontally at 14 m/s. The ball rebounds in the opposite direction with a speed of 7 m/s.

**Part A. Find the angular speed of the bar just after the collision.**

I tried to solve using conservation of angular momentum (it must be a calculation error but I keep getting the same answer):

m1v_0d = -m1vd +(1/3)m2L^2(omega)

(4.0kg)(14m/s)(1.3m) = -(3kg)(7m/s)(1.3m)+(1/3)(90N/9.82m/s)(2.5m)^2(omega)

72.8 = 57.398 + (-27.3)

1001.1 = 57.398

1.7439rad/s = \omega

**2. A Ball Rolling Uphill.**A bowling ball rolls without slipping up a ramp that slopes upward at an angle beta to the horizontal. Treat the ball as a uniform, solid sphere, ignoring the finger holes.

**Part A. What is the acceleration of the center of mass of the ball?**

I tried drawing it out, f = mew N, N = wsin(beta)

- (WsinF+ muWcos(beta) = macm

I entered acm = -g(sinF+mucos (beta)

It was incorrect, so I thought I over-did it, and tried just -g(sin(beta)), but that was also incorrect, I'm not sure where to go from here.

**Part B. What minimum coefficient of static friction is needed to prevent slipping?**

I tried mu = tan (beta)