Rotational dynamics refers to the study of rotational motion of a body along axes, under the action of torque.
To measure the angular position, we need a reference line fixed in the body also rotating with the body, and perpendicular to axes of rotation.
In the above diagram, point O is the axes of rotation. And, is the angular position, which is measured in radians. And, r is the radius.
Angular displacement is the measure of the angle in radian, by which the position of point changed.
is the angular displacement between position and
Average angular velocity of the body with angular displacement during the time interval would be:
Angular acceleration could be calculated by taking the ratio of change in angular velocity and time interval .
The following equations are true for the constant acceleration.
Question 1: Calculate the angular displacement of a student running on a circular field, with a radius of 35 m, and the student has covered a 50 m distance from his starting point.
Explanation: The radius of curvature is 35 m, and the distance traveled is 50 m.
And, we have ,
Final answer: The angular displacement would be
Question 2: Calculate the angular velocity of a rotating body about an axis after , having a constant angular acceleration of . Initially, the object was at rest .
Explanation: We will use the equation of motion
Final answer: The angular velocity would be
Question 3: Calculate the angular acceleration of a body, which gains an angular velocity of 63 rad/s, during the first 8 seconds.
Explanation: The body was initially at rest. So, , and
Also, after ,
Final answer: The angular acceleration would be .
Rotational dynamics can be defined as angular displacement of an object in motion or refers to an object that is moving in a curved path. It involves study of rotational inertia, torque, angular velocity and angular displacement.
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Rotational dynamics refers to the study of the rotational motion of a body along axes, under the action of torque.
To solve the rotational dynamics problem, we need an understanding of the equation of rotational motion.
Equation of rotational motion:
Some other important formulas:
Where angular velocity of the body with angular displacement during the time interval , and with angular acceleration α.
The motion of the Ferris Wheel, the motion of the motor, rotational of the earth around its axes are some examples of rotational motion.
The rigid body undergoes a circular motion about an axis perpendicular to the plane and the center of the circular path lies on the same axes.
In a circular motion, the particle moves around a circular path. For example, the moon is revolving in a circular path.
However, in rotational motion, the particles move in a circular path around axes perpendicular to the plane. For example, the Ferris Wheel is rotating around its axes.
So, we can say, the circular motion and rotational motion are not exactly the same.
In rotation, the particle moves around its own axes which is perpendicular to the plane. Example: motion of the fan.
And, in revolution, the object moves in a circular path around another object. Example: Earth revolving around the Sun.