What equation is the rotational equilvalent of newton's law ? give the meaning of each symbol and state which rotational quantites are analogous to which linear quantities.
L = I *alpha
is the rotational equivalent of Newton's SECOND law.
"alpha" is the angular acceleration rate
I is the moment of inertia
L is the torque about the axis of rotation
The rotational equivalent of Newton's law in linear motion is called Newton's second law of rotational motion. It can be expressed as follows:
τ = I α
In this equation:
- τ represents the torque or moment of force, measured in Newton-meters (N·m).
- I represents the moment of inertia, which is a measure of an object's resistance to rotational motion, measured in kilogram-square meters (kg·m^2).
- α represents the angular acceleration, measured in radians per second squared (rad/s^2).
The analogy between rotational and linear quantities in this equation is as follows:
- Torque (τ) is analogous to force (F) in linear motion.
- Moment of inertia (I) is analogous to mass (m) in linear motion.
- Angular acceleration (α) is analogous to linear acceleration (a) in linear motion.
Just as force causes linear acceleration, torque causes angular acceleration. The moment of inertia plays a similar role to mass, as both describe an object's inherent resistance to motion.
The rotational equivalent of Newton's law is called Newton's second law of rotation, also known as rotational analog of force. It relates the torque applied to an object to its moment of inertia and angular acceleration.
The equation for Newton's second law of rotation is:
τ = I α
In this equation:
- τ (tau) represents the torque applied to the object. Torque is the rotational force that causes an object to rotate, measured in units of Newton-meters (Nm).
- I represents the moment of inertia of the object. Moment of inertia is a measure of an object's resistance to rotation when a torque is applied, similar to how mass is a measure of an object's resistance to linear motion. Moment of inertia is usually denoted by the symbol I and has units of kilogram-meter squared (kg·m^2).
- α (alpha) represents the angular acceleration of the object. Angular acceleration is the rate at which an object's angular velocity changes over time, measured in units of radians per second squared (rad/s^2).
The rotational quantities are analogous to their linear counterparts as follows:
- Torque (τ) is analogous to force (F) in linear motion.
- Moment of inertia (I) is analogous to mass (m) in linear motion.
- Angular acceleration (α) is analogous to linear acceleration (a) in linear motion.
Just like Newton's second law in linear motion (F = ma), Newton's second law of rotation (τ = I α) describes how the applied torque affects the rotational motion of an object, similar to how force affects the linear motion of an object.