Search results
chegg.com
- The moment of inertia plays the role in rotational kinetics that mass (inertia) plays in linear kinetics—both characterize the resistance of a body to changes in its motion. The moment of inertia depends on how mass is distributed around an axis of rotation, and will vary depending on the chosen axis.
en.wikipedia.org/wiki/Moment_of_inertia
People also ask
What is the relationship between moment of inertia and rotational energy?
How does moment of inertia affect kinetic energy?
How is kinetic energy related to angular velocity and moment of inertia?
What is moment of inertia?
Sep 12, 2022 · Learning Objectives. Describe the differences between rotational and translational kinetic energy. Define the physical concept of moment of inertia in terms of the mass distribution from the rotational axis. Explain how the moment of inertia of rigid bodies affects their rotational kinetic energy.
- 10.3: Dynamics of Rotational Motion - Rotational Inertia
The quantity \(mr^2\) is called the rotational inertia or...
- 9.5: Rotational Kinetic Energy - Physics LibreTexts
Express the rotational kinetic energy as a function of the...
- 10.3: Dynamics of Rotational Motion - Rotational Inertia
The moment of inertia is the quantitative measure of rotational inertia, just as in translational motion, and mass is the quantitative measure of linear inertia—that is, the more massive an object is, the more inertia it has, and the greater is its resistance to change in linear velocity.
- Energy in A Boomerang
- Strategy
- Solution
- Significance
A person hurls a boomerang into the air with a velocity of 30.0 m/s at an angle of 40.0∘40.0∘ with respect to the horizontal (Figure). It has a mass of 1.0 kg and is rotating at 10.0 rev/s. The moment of inertia of the boomerang is given as I=112mL2I=112mL2 where L=0.7mL=0.7m. (a) What is the total energy of the boomerang when it leaves the hand? (...
We use the definitions of rotational and linear kinetic energy to find the total energy of the system. The problem states to neglect air resistance, so we don’t have to worry about energy loss. In part (b), we use conservation of mechanical energy to find the maximum height of the boomerang.
Moment of inertia: I=112mL2=112(1.0kg)(0.7m)2=0.041kg⋅m2I=112mL2=112(1.0kg)(0.7m)2=0.041kg⋅m2.Angular velocity: ω=(10.0rev/s)(2π)=62.83rad/sω=(10.0rev/s)(2π)=62.83rad/s.The rotational kinetic energ...We use conservation of mechanical energy. Since the boomerang is launched at an angle, we need to write the total energies of the system in terms of its linear kinetic energies using the velocity i...In part (b), the solution demonstrates how energy conservation is an alternative method to solve a problem that normally would be solved using kinematics. In the absence of air resistance, the rotational kinetic energy was not a factor in the solution for the maximum height.
- OpenStax
- 2016
We will also define the moment of inertia, the parameter in rotational motion that is analogous to the mass in translational motion. We will evaluate the moment of inertia for a collection of discrete particles as well as for symmetric solid objects.
Define the physical concept of moment of inertia in terms of the mass distribution from the rotational axis. Explain how the moment of inertia of rigid bodies affects their rotational kinetic energy. Use conservation of mechanical energy to analyze systems undergoing both rotation and translation.
Feb 20, 2022 · The quantity \(mr^2\) is called the rotational inertia or moment of inertia of a point mass \(m\) a distance \(r\) from the center of rotation. Figure \(\PageIndex{2}\): An object is supported by a horizontal frictionless table and is attached to a pivot point by a cord that supplies centripetal force.
Express the rotational kinetic energy as a function of the angular velocity and the moment of inertia, and relate it to the total kinetic energy. Rotational kinetic energy is the kinetic energy due to the rotation of an object and is part of its total kinetic energy.
