A thin, uniform rod has one of its end mounted at 3. point P and is free to rotate about an axle that passes through P in a direction perpendicular to the figure. The rod is of length 1.0 m and mass 0.3 kg. It is released from rest at the horizontal position shown in the figure. A small ball of mass 0.1 kg is placed on a frictionless floor 1.0 m below point P such that when the rod reaches the vertical position, it just hits the ball. Assume that once the rod hits the ball, they stick together and swing up until they come to a momentary stop at an angle 0. (a) perpendicular to the figure? You can check the table on slide 27 of the lecture notes if needed. (b) problem from the perspective of energy conservation] (c) analyze the problem from the perspective of conservation of angular momentum] What is the rotational inertia of the rod about the axle passing through P and What is the angular speed of the rod just before it hits the ball? [Hint: analyze the What is the angular speed of the rod-ball system just after they collide? [Hint:
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.
![A thin, uniform rod has one of its end mounted at
3.
point P and is free to rotate about an axle that passes
through P in a direction perpendicular to the figure. The rod
is of length 1.0 m and mass 0.3 kg. It is released from rest at
the horizontal position shown in the figure. A small ball of
mass 0.1 kg is placed on a frictionless floor 1.0 m below
point P such that when the rod reaches the vertical position,
it just hits the ball. Assume that once the rod hits the ball,
they stick together and swing up until they come to a
momentary stop at an angle 0.
(a)
perpendicular to the figure? You can check the table on slide 27 of the lecture notes if needed.
(b)
problem from the perspective of energy conservation]
(c)
analyze the problem from the perspective of conservation of angular momentum]
What is the rotational inertia of the rod about the axle passing through P and
What is the angular speed of the rod just before it hits the ball? [Hint: analyze the
What is the angular speed of the rod-ball system just after they collide? [Hint:
What is the angle 0 when the rod-ball system comes to a momentary stop? [Hint:
(d)
again analyze the problem from the perspective of energy conservation]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F32fa5d6c-9c5b-4d1e-8766-3fabf2e02b29%2F8b3551b7-bb0f-4b4d-afae-422c4061a776%2Fwaazowg_processed.jpeg&w=3840&q=75)
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