Question

Which of the following relations is wrong?

• A. Torque = Moment of inertia × Angular acceleration
• B. Torque = Magnetic moment × Magnetic field
• C. Moment of inertia = Torque × Angular acceleration
• D. Linear momentum = Moment of inertia × Angular velocity

Answer 1

Answer: (A), (B), (D)

Linear momentum = Moment of inertia × Angular velocity

The explanation for the correct options:

In the case of options A, B, and D,

1. The Torque in rotational motion is equivalent to force in linear motion. It is the prime parameter that keeps an object under rotatory motion. The torque applied to an object begins to rotate it with an acceleration inversely proportional to its moment of inertia.
2. Mathematically, it can be expressed as,

$T=I\alpha$, Where, $I$ is a moment of inertia and, $\alpha$ is angular acceleration.

Angular momentum is defined as the property of any rotating object given by moment of inertia times angular velocity.

1. Mathematically, it can be expressed as, $\overrightarrow{L}=I\times \overrightarrow{\omega }$, Where, $\overrightarrow{L}$ is the Angular momentum, $I$ is the moment of inertia, and $\overrightarrow{\omega }$ is the angular velocity.
2. The Torque in rotational motion is equivalent to force in linear motion. It is the prime parameter that keeps an object under rotatory motion. The torque applied to an object begins to rotate it with an acceleration inversely proportional to its moment of inertia. Mathematically, it can be expressed as,

$T=I\alpha$, Where, $I$ is a moment of inertia and, $\alpha$ is angular acceleration.

4. Magnetic moment, also known as magnetic dipole moment, is the measure of the object’s tendency to align with a magnetic field.

5. The magnetic moment is a vector relating torque $\left(\tau \right)$ of an object to the magnetic field. This is mathematically represented as:

$\tau =m\times B$, where, $m$ is the magnetic dipole moment, $B$ is the external magnetic field, and, $\tau$ is the torque acting on the dipole.

Hence, options (A),(B), and (D) are correct.