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A round object rolls without slipping down a slope as shown in the figure. The object starts from rest at a height of h= 1 m. The object has mass m = 2 kg and radius = 10 cm. a. What is the moment of inertia, I, if the object is: i. a solid sphere? ii. a disk? iii. a hoop? b. Using energy conservation, find the velocity of the center of mass vem of the object at the bottom of the slope for each shape (sphere, disk, hoop). c. In a race, which shape would win? h

A round object rolls without slipping down a slope as shown in the figure. The object starts from rest at a height of h= 1 m. The object has mass m = 2 kg and radius = 10 cm. a. What is the moment of inertia, I, if the object is: i. a solid sphere? ii. a disk? iii. a hoop? b. Using energy conservation, find the velocity of the center of mass vem of the object at the bottom of the slope for each shape (sphere, disk, hoop). c. In a race, which shape would win? h

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**Problem 3:** A round object rolls without slipping down a slope as shown in the figure. The object starts from rest at a height of \( h = 1 \, \text{m} \). The object has mass \( m = 2 \, \text{kg} \) and radius \( r = 10 \, \text{cm} \). **a.** What is the moment of inertia, \( I \), if the object is: i. a solid sphere? ii. a disk? iii. a hoop? **b.** Using energy conservation, find the velocity of the center of mass \( v_{cm} \) of the object at the bottom of the slope for each shape (sphere, disk, hoop). **c.** In a race, which shape would win? **Diagram Explanation:** The diagram illustrates a slope with a round object rolling down it. The slope is inclined, and the starting height of the object is labeled as \( h \). There are three shapes shown on the slope: a solid sphere, a disk, and a hoop. The illustration is meant to depict the concept of rolling motion without slipping, relevant to solving the problem.
Transcribed Image Text:**Problem 3:** A round object rolls without slipping down a slope as shown in the figure. The object starts from rest at a height of \( h = 1 \, \text{m} \). The object has mass \( m = 2 \, \text{kg} \) and radius \( r = 10 \, \text{cm} \). **a.** What is the moment of inertia, \( I \), if the object is: i. a solid sphere? ii. a disk? iii. a hoop? **b.** Using energy conservation, find the velocity of the center of mass \( v_{cm} \) of the object at the bottom of the slope for each shape (sphere, disk, hoop). **c.** In a race, which shape would win? **Diagram Explanation:** The diagram illustrates a slope with a round object rolling down it. The slope is inclined, and the starting height of the object is labeled as \( h \). There are three shapes shown on the slope: a solid sphere, a disk, and a hoop. The illustration is meant to depict the concept of rolling motion without slipping, relevant to solving the problem.
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