A particle follows a path of which the radial position is described by r = (0.2 + 0.15 case) m.. Calculate the magnitude of the particles 19992 acceleration when 0 = 30° 0 = 0.7 rad /sec, and d 0 0.5 rad/sec² in misec²9bolimpor ant staluolo 2
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
![**Title:** Calculation of Particle Acceleration in Polar Coordinates
**Description:**
A particle follows a path along which the radial position is given by the equation:
\[ r = (0.2 + 0.15 \cos \theta) \, \text{m} \]
The task is to calculate the magnitude of the particle's acceleration given the following conditions:
- The angle \( \theta = 30^\circ \)
- The angular velocity \( \dot{\theta} = 0.7 \, \text{rad/sec} \)
- The angular acceleration \( \ddot{\theta} = 0.5 \, \text{rad/sec}^2 \)
**Objective:**
To determine the particle's acceleration in meters per second squared (\( \text{m/s}^2 \)) under the specified conditions.
**Instructions:**
1. Use the provided radial and angular values.
2. Apply the relevant equations for polar coordinates to find the acceleration.
3. Ensure to express the final result in \( \text{m/s}^2 \).
**Note:** Diagrams or graphs are not present in the given text.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12c62ea9-2423-4a35-a6cd-74646c6bbd41%2F1616fbaa-ee50-49e9-8a99-3e5c09c36f2d%2Fmvubipg_processed.jpeg&w=3840&q=75)
Acceleration: The rate at which an object's velocity with respect to time changes is referred to as acceleration in mechanics. It is a vector quantity to accelerate.
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