An empty cylindrical barrel is open at one end and rolls without slipping straight down a hill. The barrel has a mass of 23.0 kg, a radius of 0.280 m, and a length of 0.700 m. The mass of the end of the barrel equals a fifth of the mass of its side, and the thickness of the barrel is negligible. The acceleration due to gravity is g = 9.80 m/s². What is the translational speed up of the barrel at the bottom of the hill if released from rest at a height of 13.0 m above the bottom? Uf = Incorrect m/s Suppose a lid was added to the barrel that had the same mass as its other end. Would adding the lid to the barrel increase, decrease, or not change the barrel's speed at the bottom of the hill if the barrel was released from the same height? Explain. The speed would decrease because the barrel's overall moment of inertia is increased, resulting in more of the initial potential energy being converted to rotational rather than translational kinetic energy. The speed would not change because mass terms ultimately cancel in the energy conservation equations, resulting in kinematic expressions that are independent of mass. The speed would increase because the distribution of the additional mass results in a fractional increase in the barrel's translational kinetic energy over its rotational kinetic energy.
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.
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
