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Chapter 8: Problem 71

The mass of a flywheel is \(5.6 \times 10^{4} \mathrm{kg} .\) This particular flywheel has its mass concentrated at the rim of the wheel. If the radius of the wheel is \(2.6 \mathrm{m}\) and it is rotating at 350 rpm, what is the magnitude of its angular momentum?

Short Answer

Expert verified
Answer: The magnitude of the flywheel's angular momentum is approximately 1.3837 * 10^7 kg*m^2/s.

Step by step solution

01

Determine the moment of inertia of the flywheel

Using the formula for a hoop's moment of inertia, calculate the moment of inertia (I) of the flywheel: I = MR^2 M = 5.6 * 10^4 kg (mass of the flywheel) R = 2.6 m (radius of the flywheel) I = (5.6 * 10^4 kg) * (2.6 m)^2 I = 3.7776 * 10^5 kg * m^2 (moment of inertia)
02

Convert rotational speed to angular velocity

The given rotational speed of the flywheel is 350 rpm. To convert rpm to radians per second, we can use the formula: ω = (2 * π radians * rotational_speed) / 60 seconds rotational_speed = 350 rpm ω = (2 * π * 350) / 60 ω ≈ 36.65 rad/s (angular velocity)
03

Calculate the angular momentum

Now that we have the moment of inertia and angular velocity, we can calculate the angular momentum (L) of the flywheel using the formula: L = Iω L = (3.7776 * 10^5 kg*m^2) * (36.65 rad/s) L ≈ 1.3837 * 10^7 kg*m^2/s The magnitude of the flywheel's angular momentum is approximately 1.3837 * 10^7 kg*m^2/s.

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Most popular questions from this chapter

A bowling ball made for a child has half the radius of an adult bowling ball. They are made of the same material (and therefore have the same mass per unit volume). By what factor is the (a) mass and (b) rotational inertia of the child's ball reduced compared with the adult ball?
The string in a yo-yo is wound around an axle of radius \(0.500 \mathrm{cm} .\) The yo-yo has both rotational and translational motion, like a rolling object, and has mass \(0.200 \mathrm{kg}\) and outer radius \(2.00 \mathrm{cm} .\) Starting from rest, it rotates and falls a distance of \(1.00 \mathrm{m}\) (the length of the string). Assume for simplicity that the yo-yo is a uniform circular disk and that the string is thin compared to the radius of the axle. (a) What is the speed of the yo-yo when it reaches the distance of $1.00 \mathrm{m} ?$ (b) How long does it take to fall? [Hint: The transitional and rotational kinetic energies are related, but the yo-yo is not rolling on its outer radius.]
A large clock has a second hand with a mass of \(0.10 \mathrm{kg}\) concentrated at the tip of the pointer. (a) If the length of the second hand is $30.0 \mathrm{cm},$ what is its angular momentum? (b) The same clock has an hour hand with a mass of \(0.20 \mathrm{kg}\) concentrated at the tip of the pointer. If the hour hand has a length of \(20.0 \mathrm{cm},\) what is its angular momentum?
A crustacean (Hemisquilla ensigera) rotates its anterior limb to strike a mollusk, intending to break it open. The limb reaches an angular velocity of 175 rad/s in \(1.50 \mathrm{ms} .\) We can approximate the limb as a thin rod rotating about an axis perpendicular to one end (the joint where the limb attaches to the crustacean). (a) If the mass of the limb is \(28.0 \mathrm{g}\) and the length is \(3.80 \mathrm{cm}\) what is the rotational inertia of the limb about that axis? (b) If the ex-tensor muscle is 3.00 mm from the joint and acts perpendicular to the limb, what is the muscular force required to achieve the blow?
The distance from the center of the breastbone to a man's hand, with the arm outstretched and horizontal to the floor, is \(1.0 \mathrm{m} .\) The man is holding a 10.0 -kg dumbbell, oriented vertically, in his hand, with the arm horizontal. What is the torque due to this weight about a horizontal axis through the breastbone perpendicular to his chest?
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