A 9.58-m ladder with a mass of 22.2 kg lies flat on the ground. A painter grabs

Question

A 9.58-m ladder with a mass of 22.2 kg lies flat on the ground. A painter grabs the top end of the ladder and pulls straight upward with a force of 264 N. At the instant the top of the ladder leaves the ground, the ladder experiences an angular acceleration of 1.62 rad/s2 about an axis passing through the bottom end of the ladder. The ladder's center of gravity lies halfway between the top and bottom ends.
(a) What is the net torque acting on the ladder?
_____ N · m

(b) What is the ladder's moment of inertia?
_____ kg · m2

Explanation / Answer

Part A)

The net torque will be the force times moment arm of the upward pull minus the force times moment arm of the weight of the ladder acting at its center of mass

= (264)(9.58) - (22.2)(9.8)(4.79)

= 1487 Nm

Part B

= I

1487 = I(1.62)

I = 918 kgm2

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