Let’s Torque

Equilibrium (again)• Its rotation is not speeding up or slowing down.

• AT REST.

• or CONSTANT ANGULAR VELOCITY.

ΣFx = 0 ΣFy = 0 Στ = 0

Your child is sitting at the end of a really heavy see-saw of total length 4m, and wants you to balance him

horizontally. How far should you sit from the fulcrum, which is at the see-saw’s center?

Child(25kg)

You (60kg)

“Balancing something” problems

[DRAW FREE BODY DIAGRAM!]

Pick the right axis(put it at the location of a force you don’t know!).

Sum forces, sum the torques, set them equal to zero.

Solve.

Where would you put your axis?Mary is about to do a push-up. Her center of gravity lies directly above a point on the floor which is d1=1.0 m from her feet and d2=0.7 m from

her hands. If her mass is 50 kg, what is the force exerted by the floor on her hands, assuming that she holds this position?

If an object is in equilibrium (she is), you can take the axis of rotation to be anywhere. The trick here is to set it somewhere that you don’t

know the force. Then sum the torques which is equal to 0.

Holding this position

A. At toesB. At handsC. At center of gravityD. None of the above

Q88

A. T = w sin θ

B. T = w cos θ

C. T = w/(sin θ)

D. T = w/(cos θ)

E. none of the above

A metal advertising sign (weight w) is suspended from the end of a massless rod of length L. The rod is supported at one end by a hinge at point P and at the other end by a cable at an angle θ from the horizontal.

What is the tension in the cable?

Q89

[DRAW FREE BODY DIAGRAM!]

Pick the right axis.

Sum forces, sum the torques, set them equal to zero.

Solve.