You are building a display for a children's science museum in which a uniform, solid sphere of radius 0.088 m starts at rest at the top of a "hill" and rolls, without slipping, down a track and around a loop-the-loop of radius R = 1.76 m. You have already determined that the ball has to be moving at a speed no less than 4.05 m/s at the top of the loop in order to make it around the loop without falling. Note: You should consider whether the ball will be above or below the track at the top of the loop. What is the minimum height of the "hill" in order to ensure that this happens?
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
You are building a display for a children's science museum in which a uniform, solid sphere of radius 0.088 m starts at rest at the top of a "hill" and rolls, without slipping, down a track and around a loop-the-loop of radius R = 1.76 m. You have already determined that the ball has to be moving at a speed no less than 4.05 m/s at the top of the loop in order to make it around the loop without falling. Note: You should consider whether the ball will be above or below the track at the top of the loop.
What is the minimum height of the "hill" in order to ensure that this happens?
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