- #1
dirk_mec1
- 761
- 13
Homework Statement
Homework Equations
Formulas for a_r and a_theta.
The Attempt at a Solution
I got the second derative of r but I think the fluxie v is a mistake. I am sure that
[itex] \dot{v} =a\ [/itex], right?
Kinematics is the branch of physics that studies the motion of objects without considering the causes of the motion.
A kinematic particle is a point-like object that is used to represent a larger object in motion, where the size and shape of the object are not important.
To derive a_r and a_theta, you must first determine the position, velocity, and acceleration of the particle in polar coordinates. Then, use the equations a_r = (v^2)/r and a_theta = (d^2θ)/(dt^2) to calculate the radial and tangential components of acceleration.
a_r represents the component of acceleration in the radial direction, while a_theta represents the component of acceleration in the tangential direction. a_r causes the particle to move closer to or further away from the origin, while a_theta causes the particle to change its direction of motion.
a_r and a_theta can be used to understand the motion of objects in circular or curved paths, such as a car turning a corner or a planet orbiting around a star. They can also be used in the design and analysis of machines and structures that involve rotational motion.