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Chapter 12: Q. 24 (page 331)
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?
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In FIGURE CP12.88, a 200 g toy car is placed on a narrow 60-cm-diameter track with wheel grooves that keep the car going in a circle. The 1.0 kg track is free to turn on a frictionless, vertical axis. The spokes have negligible mass. After the car’s switch is turned on, it soon reaches a steady speed of 0.75 m/s relative to the track. What then is the track’s angular velocity, in rpm?
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 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 μg rigid rod with a 10 μg anther sac at the end. Although oversimplifying, we’ll assume a constant angular
acceleration.
a. How large is the “straightening torque”?
b. What is the speed of the anther sac as it releases its pollen?
33. II A car tire is 60 cm in diameter. The car is traveling at a speed of 20 m/s.
a. What is the tire's angular velocity, in rpm?
b. What is the speed of a point at the top edge of the tire?
c. What is the speed of a point at the bottom edge of the tire?
A V -diameter turntable rotates at on frictionless bearings. Two blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter, and stick. What is the turntable's angular velocity, in rpm, just after this event?
Consider a solid cone of radius R, height H, and mass M. The volume of a cone is 1/3 πHR2
a. What is the distance from the apex (the point) to the center of mass?
b. What is the moment of inertia for rotation about the axis of the cone?
Hint: The moment of inertia can be calculated as the sum of the moments of inertia of lots of small pieces.
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