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

Torque due to Gravity The torque due to a uniform gravitational field is calculated as if the entire gravitational force is applied at the center of gravity.

Torque due to Gravity Equilibrium Problem 2 A rigid bar of length one meter and mass 5 kg is connected to a hinge. If one was to apply a force on the right end of the bar, what would the magnitude and direction of this force need to be to prevent the bar from rotating clockwise?

Torque due to Gravity Problem 3 A board has a length of 80 cm and a weight of 3 N. A 1 N apple is placed at the 10 cm position, a 2 N orange is placed at the 30 cm position, and a 7 N loaf of bread is placed at the 70 cm position. What force must one apply to balance the board? At what position on the board must the force be applied?

13 N 52 cm

Problem 4: 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