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Rotational Motion

Spinning Top Why a spinning top doesn’t fall over? This image shows a top that is in action after its release. Doesn't it seem it is defying gravity while it is spinning? If spun fast enough, a spinning top will rise to a vertical position and continue to spin, despite the fact that it will fall over if it stops spinning. The basic physics behind this is that a torque is required to rotate an object. The torque(force) is equal to the rate of change of angular momentum, which is the rotational equivalent of what happens when an object accelerates along a straight line. Angular momentum is similar to linear momentum, but it refers to motion in a circular rather than a straight line path. Lets learn more about the Moment of Inertia and Angular momentum of an object, in detail.

Learning Objectives

After completing the topic, the student will be able to:

  • Understand, discuss and explore about the rotatory motion and apply it to real world situations.
  • Define and discuss various terms like angular displacement, angular velocity, angular acceleration, time period of rotation, moment of inertia, angular momentum, radius of gyration, torque, etc.
  • Develop equations of motion for both rotational and linear motion.
  • Understand vector nature of angular variables and the concept of torque.
  • Explore and illustrate Newton’s second law for rotational motion.
  • Understand and explore angular momentum and its conservation.
  • Explore about the moment of inertia leading to parallel axis and perpendicular axis theorems.
Rotational Motion of the helicopter blades Rotational motion of the helicopter blades Motion of a helicopter blades is an example of rotational motion
Rotational Motion

The motion of a Ferris wheel, ceiling fan and the rotating helicopter blade are all examples of rotational motion. They rotate about an axis that is stationary in some inertial frame of reference. Rotation occurs even in planets and galaxies. Rotation around a fixed axis is a special case of rotational motion. Earth rotating around its axis is an example for rotation around a fixed axis.

We have seen that there are different types of motions: translational, rotational and oscillatory (or vibrational). We discussed details of translational motion when we studied Linear and Non-linear motions. These were essentially one and two–dimensional motions of a body. For the basic understanding of motion, we simplified our discussions by considering the body in motion as just one point. All particles in the body in motion, moved parallel to each other.

Center of mass for symmetrical bodies Center of mass for symmetrical bodies
  • CM of a square is at the point of intersection of its diagonals.
  • CM of a sphere is at its centre.
  • CM of a rigid bar is at the middle point.
Study of motion vis-a-vis CM

We have learnt that the centre of mass (CM) for symmetrical bodies is located at its geometric centre. Implicitly we understood all concepts of motion based on the motion of this particular point. We proceeded to understand complex two–dimensional motions, such as projectile motion and circular motion, by studying the motion of CM. We have always been restricting our examples to objects that were either point–like or symmetrical in shape, such as a ball or a coin, etc. This did not disturb our understanding of any of the fundamental concepts of motion.

Now let us go a notch higher into the real world. After all, an object in motion is not a point particle. It has dimensions. The first step for this level of knowledge is to know what is CM of a body. CM of a body is defined as the point at which the entire mass of a body can be assumed to be concentrated for determining the motion of the body under the action of external forces. CM of a body can be determined by its geometrical considerations. If a body is symmetrical and of uniform composition, the CM will be located at its geometrical centre.

If a body is irregularly shaped or if its density is unevenly distributed, its CM is not easy to locate, but still it can be done using many experimental techniques.

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