A lump of putty (0.050 kg) hits a contraption that is made of a uniform solid cylinder rotating about its center of mass and two rods that are attached to the sides of the cylinder. The moment of inertia of the contraption is 0.250 kg∙m2. After the collision, the putty attaches to the contraption 0.15 m from the axis of rotation and the combination is rotating at 1.0 rad/s. Determine the linear speed of the putty before the collision. Determine the angular impulse on the putty and on the block separately to show that they follow Newton’s 3rd law. How much energy is lost in the collision? Where did it go?
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 lump of putty (0.050 kg) hits a contraption that is made of a uniform solid cylinder rotating about its center of mass and two rods that are attached to the sides of the cylinder. The moment of inertia of the contraption is 0.250 kg∙m2. After the collision, the putty attaches to the contraption 0.15 m from the axis of rotation and the combination is rotating at 1.0 rad/s.
- Determine the linear speed of the putty before the collision.
- Determine the angular impulse on the putty and on the block separately to show that they follow Newton’s 3rd law.
- How much energy is lost in the collision? Where did it go?
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