Spinning in figure skating, dance, gymnastics, and diving is a good example of accelerating or decelerating the athlete’s body by changing the moment of inertia. To increase torque the athlete can apply greater force when hitting a soccer ball to move along a curve To accelerate or decelerate the object we can also apply force to it. Thus, we can change the moment of inertia by modifying the mass of the object or this radius. It is influenced by the weight and the shape of the object, in particular - the radius from the center of rotation to the point of the object that is furthest away from this center.

In some cases, it is easier to change the moment of inertia. In particular, to accelerate an object we need to increase the force that prompts the rotation or to decrease the moment of inertia. The relationship described above between angular acceleration, moment of inertia, and torque shows that we can manipulate acceleration using the other two parameters. In other words, this relationship between the tendency to rotate and the resistance to rotation is equivalent to the relationship for linear motion, outlined by Newton’s Second Law: F = ma, where a is linear acceleration, F is the force that makes the body move, and m is the mass, which corresponds to the resistance to this movement by the object. Here torque refers to the tendency of objects to rotate when a force is applied to them, while the moment of inertia is the resistance to this rotating motion. On the other hand, angular acceleration is calculated by dividing torque by the moment of inertia.

The greater this radius is - the smaller the centripetal acceleration. The radius here refers to the distance from the object to the center of rotation. In particular, centripetal acceleration is tangential velocity squared, divided by the radius. We also have to be careful when calculating angular acceleration and not to confuse it with the calculations for centripetal acceleration. Angular acceleration, on the other hand, relates to the force that is applied to the object to propel it forward. An example of this force can be seen in roller coasters: centripetal force keeps the cars from falling down, even if they are moving upside-down along a circular trajectory. It is always directed towards the center of rotation and keeps the object moving along the curve. The centripetal acceleration relates to the centripetal force as we mentioned above. If we relate the acceleration to the force, we will see another difference between the centripetal and the angular acceleration. Angular and centripetal accelerations are, therefore, perpendicular. Centripetal acceleration, on the other hand, is directed toward the center of rotation and thus is perpendicular to the direction of the movement. It is marked in pink (A) in the illustration. It is marked in dark blue (B) on the illustration.Īngular acceleration is parallel to the force that is pushing the object to move along the curve and is perpendicular to the radius of rotation. Here the tangential velocity is the linear speed of an object at each given moment of time, which is the velocity that the object would have if it were moving along the tangent. Unlike the angular acceleration, the centripetal acceleration indicates the rate of change of the velocity along the tangent of the path of rotation, known as tangential velocity. In the illustration, the centripetal force is marked in purple (C) and the centripetal acceleration is marked in light blue (D). This happens because both angular and centripetal accelerations are used to describe circular movement. The angular acceleration is often confused with the centripetal acceleration caused by the centripetal force. It creates centripetal acceleration D (light blue), also directed towards the center Besides the external force pushing it, centripetal force C (purple), directed towards the center of rotation, acts on the object. Its tangential velocity is B (dark blue). The orange object is moving along the circle with angular acceleration A, shown in pink.

Rad to rpm