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Chapter 12: Q. 9 (page 330)

A thin, 100g disk with a diameter of 8.0 cm rotates about an axis through its center with 0.15 J of kinetic energy. What is the speed of a point on the rim?

Short Answer

Expert verified

The speed of a point on the rim is2.4m/s

Step by step solution

01

Step 1. Given information

Radius of rim, R=0.040mMass of rim, M=0.10kgRotational kinetic energy, K=0.15J

02

Step 2. Explanation

The moment of inertia of the disk

I=12MR2=12(0.10kg)(0.040m)2=8.0×10−5kgm2

The rotational kinetic energy

K=12Iω2=0.15Jω2=2(0.15J)I=0.30J8.0×10−5kgm2ω=61.237rad/s

The speed of a point on the rim

.vrim=Rω=(0.040m)(61.237rad/s)=2.4m/svrim=Rω=(0.040m)(61.237rad/s)=2.4m/s

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Most popular questions from this chapter

A 200 g, 40-cm-diameter turntable rotates on frictionless bearings at 60 rpm. A 20 g block sits at the center of the turntable. A compressed spring shoots the block radially outward along a frictionless groove in the surface of the turntable. What is the turntable’s rotation angular velocity when the block reaches the outer edge?

35. II An 8.0-cm-diameter, 400g solid sphere is released from rest at the top of a 2.1-m-long, 25°incline. It rolls, without slipping, to the bottom.

a. What is the sphere's angular velocity at the bottom of the incline?

b. What fraction of its kinetic energy is rotational?

The 3.0-m-long, 100 kg rigid beam of FIGURE EX12.31 is supported at each end. An 80 kg student stands 2.0 m from support 1. How much upward force does each support exert on the beam?

A rod of length L and mass M has a nonuniform mass distribution. The linear mass density (mass per length) is λ= cx2, where x is measured from the center of the rod and c is a constant.

a. What are the units of c?
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The three masses shown in FIGURE EX12.15 are connected by massless, rigid rods.

a. Find the coordinates of the center of mass.

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c. Find the moment of inertia about an axis that passes through masses B and C.
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