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Ch. 10 - Rotational Motion
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 10 - Rotational MotionProblem 79a
Chapter 10, Problem 79a

The 1100-kg mass of a car includes four tires, each of mass 35 kg (including wheels) and diameter 0.80 m. Assume each tire and wheel combination acts as a solid cylinder. Determine the total kinetic energy of the car when traveling 95 km/h.

Verified step by step guidance
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Convert the car's speed from km/h to m/s. Use the conversion factor: \(1 \ \text{km/h} = \frac{1000}{3600} \ \text{m/s}\).
Calculate the translational kinetic energy of the car using the formula \(KE_{\text{trans}} = \frac{1}{2} m v^2\), where \(m\) is the total mass of the car (including the tires) and \(v\) is the speed in m/s.
Determine the rotational kinetic energy of one tire using the formula \(KE_{\text{rot}} = \frac{1}{2} I \omega^2\), where \(I\) is the moment of inertia of a solid cylinder \(I = \frac{1}{2} m r^2\), and \(\omega = \frac{v}{r}\) is the angular velocity. Here, \(r\) is the radius of the tire (half the diameter).
Multiply the rotational kinetic energy of one tire by 4 to account for all four tires.
Add the translational kinetic energy of the car and the total rotational kinetic energy of the tires to find the total kinetic energy of the car.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 0.5 * m * v^2, where m is the mass and v is the velocity. In this context, the car's total kinetic energy will include both the translational kinetic energy of the car's body and the rotational kinetic energy of its tires.
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Intro to Rotational Kinetic Energy

Translational vs. Rotational Motion

Translational motion refers to the movement of an object from one location to another, while rotational motion involves an object spinning around an axis. For the car, the translational motion is its forward movement, and the rotational motion pertains to the spinning of the tires, which must be accounted for when calculating total kinetic energy.
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Solid Cylinder Moment of Inertia

The moment of inertia is a measure of an object's resistance to changes in its rotation and is crucial for calculating the rotational kinetic energy. For a solid cylinder, the moment of inertia is given by I = 0.5 * m * r^2, where m is the mass and r is the radius. This concept is essential for determining the kinetic energy associated with the rotation of the car's tires.
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Related Practice
Textbook Question

A cyclist accelerates from rest at a rate of 1.00 m/s². How fast will a point at the top of the rim of the tire (diameter = 68.0 cm) be moving after 2.75 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest—see Fig. 10–69.]

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Textbook Question

On a 12.0-cm-diameter audio compact disc (CD), digital bits of information are encoded sequentially along an outward spiraling path. The spiral starts at radius R₁ = 2.5 cm and winds its way out to radius R₂ = 5.8 cm. To read the digital information, a CD player rotates the CD so that the player’s readout laser scans along the spiral’s sequence of bits at a constant linear speed of 1.25 m/s. Thus the player must accurately adjust the rotational frequency ƒ of the CD as the laser moves outward. Determine the values for ƒ (in units of rpm) when the laser is located at R₁ and when it is at R₂.

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Textbook Question

A solid rubber ball rests on the floor of a railroad car when the car begins moving with acceleration a. Assuming the ball rolls without slipping, what is its acceleration relative to the car?

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Textbook Question

The 1100-kg mass of a car includes four tires, each of mass 35 kg (including wheels) and diameter 0.80 m. Assume each tire and wheel combination acts as a solid cylinder. Determine the fraction of the kinetic energy in the tires and wheels.

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Textbook Question

A solid rubber ball rests on the floor of a railroad car when the car begins moving with acceleration a. Assuming the ball rolls without slipping, what is its acceleration relative to the ground?

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Textbook Question

II) A uniform solid sphere of radius r0 = 24.5 cm and mass m = 1.60 kg starts from rest and rolls without slipping down a 30.0° incline that is 10.0 m long. Calculate its translational and rotational speeds when it reaches the bottom. Avoid putting in numbers until the end so you can answer.

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