The objects listed are placed at the top of a ramp and roll down to the bottom without slipping. Assuming that there is no air resistance, rank them in order from fastest average rolling speed to slowest. Bowling ball, hollow globe, penny, and wedding ring.
To rank the objects from fastest average rolling speed to slowest, we need to consider the moment of inertia for each object. The moment of inertia determines how mass is distributed around the rotation axis of an object, affecting its rolling motion.
Generally, objects with lower moments of inertia will roll faster. The moment of inertia depends on both the mass and the distribution of mass around the axis of rotation. In this case, assuming all objects have the same radius, we will rank them based on their mass distribution.
1. Penny: The penny has a small mass and a relatively thin and uniform distribution. Therefore, it will have the lowest moment of inertia and roll the fastest among the listed objects.
2. Wedding ring: A wedding ring typically has a small mass, similar to a penny. However, it is also thin and hollow, which increases its moment of inertia compared to the penny. Consequently, the wedding ring will roll slower than the penny.
3. Hollow globe: The hollow globe has a larger mass and a more uniform distribution compared to the penny or the wedding ring. It will have a higher moment of inertia than the previous two objects, contributing to a slower rolling speed.
4. Bowling ball: The bowling ball has the largest mass and a dense distribution of mass. Its moment of inertia will be significantly higher than the other three objects mentioned, causing it to have the slowest average rolling speed.
Therefore, the objects ranked from fastest average rolling speed to slowest are: Penny, Wedding ring, Hollow globe, Bowling ball.
To determine the order of the objects from fastest to slowest average rolling speed, we need to consider the concept of rotational inertia, also known as the moment of inertia. It is a property of objects that relates to how their mass is distributed around their axis of rotation.
The formula to calculate the rotational inertia of a rolling object is:
I = 2/5 * m * r^2
Where:
- I represents the rotational inertia
- m represents the mass of the object
- r represents the radius of the object
Now let's analyze each object based on its rotational inertia and determine their ranking:
1. Hollow Globe:
A hollow globe has a large radius compared to its mass. Due to its distribution of mass farther from its axis of rotation, it would have the smallest moment of inertia among the given objects. Therefore, it will have the fastest average rolling speed.
2. Bowling Ball:
A bowling ball has a slightly smaller radius than a hollow globe but has a higher mass. Although it has more mass, the smaller difference in radius compared to the hollow globe results in a slightly higher rotational inertia. Thus, the bowling ball will have the second fastest average rolling speed.
3. Penny:
A penny is smaller and denser than the previous objects, with a smaller radius and less mass. With a mass closer to its axis of rotation, the penny would have a higher rotational inertia than both the hollow globe and the bowling ball. Therefore, its average rolling speed would be slower than those two objects.
4. Wedding Ring:
A wedding ring is the smallest and lightest object in the list, with a very small radius. Due to its small mass and mass distribution close to its axis of rotation, it would have the highest rotational inertia compared to the other objects. Consequently, it will have the slowest average rolling speed.
Therefore, the ranking from fastest to slowest average rolling speed would be:
1. Hollow Globe
2. Bowling Ball
3. Penny
4. Wedding Ring
rank the objects in order of their moments of inertia
... from lowest to highest
the bowling ball is a solid sphere
... the globe is a hollow sphere
... the penny is a disc
... the ring is ... a ring