University:
Arizona State University
Course:
PHYS 102 | Introductory Physics I
Academic year:

2024
Views:

186

Pages:

3
Author:

Mohammed N.

Rotational Motion Rotational motion refers to the motion of a body around a fixed axis. It is an essential concept in physics as it helps describe how objects spin and rotate in various applications. 1. Angular Displacement, Velocity, and Acceleration ● Angular Displacement (θ): The angle through which an object rotates, measured in radians. ● Angular Velocity (ω): The rate of change of angular displacement, given by ω=dθ/dt(rad/s). ● Angular Acceleration (α): The rate of change of angular velocity, given by α=dω/dt(rad/s²). 2. Equations of Rotational Motion The equations of rotational motion are analogous to linear motion equations: where: ● ω0= Initial angular velocity ● ω = Final angular velocity ● α= Angular acceleration ● θ = Angular displacement ● t = Time 3. Torque and Moment of Inertia Torque is the rotational equivalent of force and is given by: τ=rFsinθ where: ● τ = Torque (N·m) ● r = Lever arm distance (m) ● F= Applied force (N) ● θ= Angle between force and lever arm Moment of inertia (I) is the rotational equivalent of mass and depends on the mass distribution of the object. 4. Rotational Kinetic Energy The kinetic energy associated with rotational motion is given by: 5. Conservation of Angular Momentum Angular momentum (L) is given by: L=Iω The principle of conservation of angular momentum states that if no external torque acts on a system, the total angular momentum remains constant: I1ω1=I2ω2 6. Applications of Rotational Motion ● Spinning of planets and celestial bodies. ● Rotational motion in machinery such as gears and turbines. ● Gyroscopes and stabilization systems. ● Sports like figure skating and gymnastics. Conclusion Rotational motion plays a crucial role in various physical systems. Understanding its principles helps in applications ranging from mechanical engineering to astrophysics and sports dynamics.