# Angular velocity and acceleration relationship goals

### Module 1 -- Angular Kinematics - PER wiki

Angular Velocity and Acceleration. Definition: Angular Velocity. Angular velocity $\omega$ of a rigid body is the rate of change of its angular position. Thus. Learning Objectives relationships among rotation angle, angular velocity, angular acceleration, is constant, which means that angular acceleration \ alpha. Introduction. What are the goals of biomechanics of sport and physical exercise? Kinematcs. Motion of bodies with constant acceleration · 20 . Relation between angular velocity and peripheral velocity. In tennis, golf, hockey, and other.

Remember, angular velocity or the magnitude of angular velocity is measured in radians per second and we typically view radians as an angle but if you think of it as an arc length, a radian you could view it as how many radii in length am I completing per second? And so, if I multiply that times the actual length of the radii, then you can get a sense of well, how much distance am I covering per second? Hopefully that makes some sense and we actually prove this formula, we get an intuition for this formula in previous videos but from this formula it's easy to make a substitution back into our original one to have en expression for centripetal acceleration, the magnitude of centripetal acceleration in terms of radius and the magnitude of angular velocity and I encourage you, pause this video and see if you can drive that on your own.

All right, let's do this together.

• Deriving formula for centripetal acceleration from angular velocity
• Oscillation with angular velocity
• Module 1 -- Angular Kinematics

So, if we start with this, we have the magnitude of our centripetal acceleration is going to be equal to, instead of putting V squared here, instead of V, I can write R omega, so let me do that, R and then omega. There you go and all I did I said look, our linear speed right over here is equal to our radius times the magnitude of our angular velocity or angular speed, so everywhere I saw a V here, I'm just replacing it with an R omega and so, I have R omega, the entire quantity squared over R and then we can simplify this.

This is going to be equal to, I just use my exponent properties here, R omega times R omega is gonna be R squared times omega squared, all of that over R. Muscles can thus contract over shorter distance to effect longer distances of motion of our extremities.

In sports such as gymnastics the more important factor of performance is mean angular velocity because it determines how many somersaults and twists the given athlete can manage. Relation between angular velocity and peripheral velocity In tennis, golf, hockey, and other sport events the instruments used make our arms longer.

### Kinematics • Kinematics of Rotary Motion

For example longer golf clubs are used for driving with higher initial velocity to longer distances. Shorter golf clubs are used for shorter distances. In the above mentioned sports there is an important concept of effective radius. For example our feet move much faster than is the speed of muscle contraction in those muscles that control the motion of legs in walking and running.

Angular Acceleration Angular acceleration is the rate of change of angular velocity over time. Mathematically we can define mean angular acceleration as: The magnitudes of tangential acceleration and angular acceleration are interrelated: Our lean, as well as the forces that incurvate the trajectory of our downhill motion, are directed towards the centre of our ski turns.

Mathematically the magnitude of centripetal acceleration can be defined as: If, for example, we are running in the first track, we have to exert greater centripetal force and thus accelerate towards the centre more than if we are running in the last track.

For this reason the friction between track shoes and the surface is greater if we are running in the first track. The direction of the angular velocity The angular velocity is a vector.

Its direction is parallel to the axis of rotation, therefore the angular velocity vector is perpendicular to the plane where the circle described by point B is contained. As shown in the figure: Note that what it looks rotating counterclockwise from one side is rotating clockwise from the other side.

## Kinematics

To obtain the correct direction of the angular velocity vector we will use the right hand rule. Use the right hand rule The direction of the angular velocity vector can be obtained by the right hand rule: Curl the fingers of your right hand along the direction of the rotation of the object, your thumb will point to the direction of the angular velocity vector.

Test your understanding Use the right hand rule to find the direction of the angular velocity vector in the situations shown in the figures below. You should take the point of view of the little man shown in the figures and calculate the direction of the disk's angular velocity using the right hand of the observer. Express your answer in terms of the given coordinate system: The direction of the angular acceleration vector The angular acceleration is a vector and its direction is either parallel or anti-parallel to the angular velocity vector.

In analogy to one dimensional motion, if the angular acceleration vector is in the same direction as the angular velocity vector then the rotation is speeding up. If the vectors are in opposite direction then the rotation is slowing down. Test your understanding The disk in the figures below rotates about the dotted fixed axis.

Each of the 4 figures above show the angular velocity and angular acceleration vectors of one of the following situations: A CD rotates clockwise as viewed from above.

After listening to your favorite song you turned the CD player off. Figure c The disk is slowing down then the angular acceleration is opposite to the angular velocity.

Following the right hand rule, a clockwise rotation as viewed from above implies an angular velocity pointing away from the observer, therefore the angular acceleration is pointing towards the observer. You now turn the CD player on.