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

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 = 0 Translational Equilibrium ∑τ = 0 Rotational Equilibrium

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

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

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=500 + 350+40 + Fp Fp=890 N

Seasaw a) 2.14 m from center b) 890 N

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.

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

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.

Leaning Ladder Problem