(a) A person holds a ladder horizontally at its center. Treating the ladder as a uniform rod of length 3.66 m and mass of 10.9 kg, find the moment of force that the person must exert on the ladder to give it an angular acceleration of 0.333 rad/s2 . The moment of inertia of a uniform rod of mass M and length L is I = 1 / 2ML2 when the axis of rotation is through its center (b) A steel bridge is constructed in the summer when its temperature is 35.0˚C. At the time of construction, its length was 80.0 m. How long is the bridge in winter when its temperature is -12.0˚C? The coefficient of thermal expansion for steel is 1.2 × 10-5 K -1. (please show steps, explanation and formulas)
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) A person holds a ladder horizontally at its center. Treating the ladder as a uniform rod of length 3.66 m and mass of 10.9 kg, find the moment of force that the person must exert on the ladder to give it an
(b) A steel bridge is constructed in the summer when its temperature is 35.0˚C. At the time of construction, its length was 80.0 m. How long is the bridge in winter when its temperature is -12.0˚C? The coefficient of thermal expansion for steel is 1.2 × 10-5 K -1.
(please show steps, explanation and formulas)
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