1. Aim: How do we explain applications of Newton’s Second Law for Rotation?

2. Rigid Body in Equilibrium
Two conditions for Complete Equilibrium of an object:
The net external force must equal zero
The net external torque must be zero about any axis
∑F = Translational Equilibrium
∑τ = Rotational Equilibrium

3. Thought Question
Is it possible to have a situation in which an object is in translational equilibrium but not rotational equilibrium? Yes, an accelerating wheel Is it possible to have a situation in which an object is in rotational equilibrium but not translational equilibrium? Yes, an object that slides while accelerating

4. Static Equilibrium
Object is at rest with no angular speed. ω=0 and vcm = 0

5. Seasaw Problem
Two children weighing 500 N and 350 N are on a uniform board weighing 40 N supported at its center. If the 500 N child is 1.50 m from the center, determine
where the 350 N child must sit to balance the system
τ1=τ2
r1F1=r2F2
1.5(500)=r(350) r=2.14 m
b) The upward force exerted on the board by the support ΣF = 0= Fp
Fp=890 N

6. Seasaw
a) 2.14 m from center b) 890 N

7. Standing on a Horizontal Beam
A uniform horizontal beam of length 8.00 m and weight 200 N is attached to a wall by a pin connection. Its far end is supported by a cable that makes an angle of 53 degrees with the horizontal. If a 600 N man stands 2.00 m from the wall, find the tension in the cable and the force exerted by the wall on the beam.

8. Standing on a Horizontal Beam
T=313 N and R=581 N

10. Leaning Ladder Problem
A uniform ladder of length l and mass m rests against a smooth, vertical wall. If the coefficient of static friction between the ladder and ground is μs=0.40, find the minimum angle θmin such that the ladder does not slip.

11. Leaning Ladder Problem