A uniform rod of mass 1.90 kg and length 2.00 m is capable of rotating about an axis passing through its center and perpendicular to its length. A mass m1 = 4.90 kg is attached to one end and a second mass m2 = 3.40 kg is attached to the other end of the rod. Treat the two masses as point particles. (a) What is the moment of inertia of the system? (Answer in kg•m^2) (b) If the rod rotates with an angular speed of 2.60 rad/s, how much kinetic energy does the system have? (Answer in J) (c) Now consider the rod to be of negligible mass. What is the moment of inertia of the rod and masses combined? (Answer in kg•m^2) (d) If the rod is of negligible mass, what is the kinetic energy when the angular speed is 2.60 rad/s? (Answer in J)
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 uniform rod of mass 1.90 kg and length 2.00 m is capable of rotating about an axis passing through its center and perpendicular to its length. A mass
is attached to one end and a second mass
is attached to the other end of the rod. Treat the two masses as point particles.
(a) What is the moment of inertia of the system? (Answer in kg•m^2)
(b) If the rod rotates with an angular speed of 2.60 rad/s, how much kinetic energy does the system have? (Answer in J)
(c) Now consider the rod to be of negligible mass. What is the moment of inertia of the rod and masses combined? (Answer in kg•m^2)
(d) If the rod is of negligible mass, what is the kinetic energy when the angular speed is 2.60 rad/s? (Answer in J)
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