A thin rod of length 0.926 m and mass 174 g is suspended freely from one end. It is pulled to one side and then allowed to swing like a pendulum, passing through its lowest position with angular speed 1.49 rad/s. Neglecting friction and air resistance, find (a) the rod's kinetic energy at its lowest position and (b) how far above that position the center of mass rises. (a) Number i (b) Number i Units Units
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.
![## Problem Statement
A thin rod of length 0.926 m and mass 174 g is suspended freely from one end. It is pulled to one side and then allowed to swing like a pendulum, passing through its lowest position with an angular speed of 1.49 rad/s. Neglecting friction and air resistance, find (a) the rod's kinetic energy at its lowest position and (b) how far above that position the center of mass rises.
### Solution
1. **Kinetic Energy Calculation (Part a):**
- Formula: \( KE = \frac{1}{2} I \omega^2 \)
- Where \( I \) is the moment of inertia and \( \omega \) is the angular speed.
2. **Height Calculation (Part b):**
- Use energy conservation principles to find the height.
### Input Fields
- (a) Kinetic Energy:
- **Number:** [Input box]
- **Units:** [Dropdown]
- (b) Height:
- **Number:** [Input box]
- **Units:** [Dropdown]
### Notes
- Ensure all calculations consider the length and mass unit conversions where necessary.
- Assume ideal conditions for energy conversion (no energy loss).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F27af745b-6d4f-4129-9ebf-5574c17547e0%2F3e9fb4ff-5111-4f9c-9356-88199772417f%2F0mryl17_processed.jpeg&w=3840&q=75)
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