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Chapter 12: Q. 37 (page 331)
Evaluate the cross products and
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An object's moment of inertia is . Its angular velocity in increasing at the rate of per second. What is the net torque on the object?
The four masses shown in FIGURE EX12.13 are connected by massless, rigid rods.
a. Find the coordinates of the center of mass.
b. Find the moment of inertia about an axis that passes through mass A and is perpendicular to the page.
A ceiling fan with 80 cm-diameter blades is turning at 60 rpm. Suppose the fan coasts to a stop 25s after being turned off.
A rod of length L and mass M has a nonuniform mass distribution. The linear mass density (mass per length) is 位= cx2, where x is measured from the center of the rod and c is a constant.
a. What are the units of c?
b. Find an expression for c in terms of L and M.
c. Find an expression in terms of L and M for the moment of inertia of the rod for rotation about an axis through the center.
The bunchberry flower has the fastest-moving parts ever observed in a plant. Initially, the stamens are held by the petals in a bent position, storing elastic energy like a coiled spring. When the petals release, the tips of the stamen act like medieval catapults, flipping through a 60o颅 angle in just 0.30 ms to launch pollen from anther sacs at their ends. The human eye just sees a burst of pollen; only high-speed photography reveals the details. As FIGURE CP12.85 shows, we can model the stamen tip as a 1.0mm long, 10 渭g rigid rod with a 10 渭g anther sac at the end. Although oversimplifying, we鈥檒l assume a constant angular
acceleration.
a. How large is the 鈥渟traightening torque鈥�?
b. What is the speed of the anther sac as it releases its pollen?
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