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The general relationship among torque, moment of inertia, and angular acceleration is \[net \, \tau = I \alpha\] or \[\alpha = \dfrac{net \, \tau}{I},\] where net \(\tau\) is the total torque from all forces relative to a chosen axis.
- Rotational Kinetic Energy
Example \(\PageIndex{1}\): Calculating the Work and Energy...
- Kinematics of Rotational Motion
This example illustrates that relationships among rotational...
- Rotational Kinetic Energy
The moment of inertia, otherwise known as the mass moment of inertia, angular/rotational mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is defined relative to a rotational axis. It is the ratio between the torque applied and the resulting angular acceleration about that axis.
This is a simulation of a circular object mounted on an axis through its center with a constant torque applied. Objects with varying rotational inertia (solid sphere, spherical shell, solid cylinder, cylindrical shell) can be chosen, and the mass and radius of the object can be adjusted.
We've looked at the rotational equivalents of displacement, velocity, and acceleration; now we'll extend the parallel between straight-line motion and rotational motion by investigating the rotational equivalent of force, which is torque.
Study the analogy between force and torque, mass and moment of inertia, and linear acceleration and angular acceleration. If you have ever spun a bike wheel or pushed a merry-go-round, you know that force is needed to change angular velocity as seen in Figure 10.9 .
20 lip 2022 · From our torque diagram, the torque about the point O at the center of the pulley is given by \[\vec{\tau}_{O}=\overrightarrow{\mathbf{r}}_{O, 1} \times \overrightarrow{\mathbf{T}}_{1}+\overrightarrow{\mathbf{r}}_{O, 2} \times \overrightarrow{\mathbf{T}}_{2}=R\left(T_{1}-T_{2}\right) \hat{\mathbf{k}} \nonumber \]
Kinematics is the study of how things move. Rotational kinematics is the study of how rotating objects move. Let’s start by looking at various points on a rotating disk, such as a compact disc in a CD player. EXPLORATION 10.1 - A rotating disk.
