Angular motion Flashcards
Define angular motion
The movement of a body or body part in a circular path around an axis of rotation
What causes angular motion
Angular motion results from an eccentric force being applied to a body where the force is applied outside the centre of bodies mass
An eccentric force is also known as a torque this is a rotational force
What is an axis of rotation
Imaginary line about which a body part turns
What is angular velocity and how is it calculated
Rate of change in angular displacement or simply the rate of rotation which can be calculated by: Angular velocity = angular displacement / time taken
Measured in radians per second
1 radian = 57.3 degrees
360 degrees = 2 pi radians
What is moment of inertia
Resistance of a body to change its state of angular motion or rotation
A resting body will not want to start rotating around an axis and the rotating body will not want to change angular momentum or velocity so it will resist increasing or decreasing the rate of spin
Moment of inertia is angular equivalent to inertia
Factors affecting size of moment of inertia and relationship
Mass: The larger mass the larger the moment of inertia, E.g. takes less torque to initiate spin on a 1kg discuss than a 2kg discus
Distribution of mass about the axis of rotation: closer the mass of a body to the axis, the smaller the moment of inertia, E.g. tuck somersault body mass is closer to transverse axis than pike
Moment of inertia size: is inversely proportional to angular motion
Smaller moment of inertia less torque needed to change its angular motion
Moment of inertia equation
MI = sum of mass X distance of mass from axis of rotation squared
What is angular momentum
Angular momentum is the quantity of angular motion possessed by a body. It is the rotational equivalent of momentum and can be calculated using the following equation :
Angle momentum = moment of inertia X angular velocity
Angle momentum is measured in kilogramme metres squared radians per second
To initiate rotation around an axis angular momentum must be generated by applying an eccentric force or torque
Conservation of angular momentum
Once angular momentum has been generated it is a product of moment of inertia and angular velocity.
As moment of inertia increases angular velocity decreases and vice versa.
This means angular momentum once generated does not change throughout a movement it remains constant and therefore is termed a conserved quantity.
This means a performer can maintain a rotation for a long period of time.
For example, an ice skater performing a flat spin.
Angular momentum during flight
Angular momentum = moment of inertia x angular velocity (Iω)
So if moment of inertia (I) decreases during flight due to body shape changes, then angular velocity (ω) must increase in order for angular momentum to stay the same. Likewise if I increases, then ω must decrease
What is this graph showing
The graphs show that angular momentum is conserved in flight, or when no external torques are acting.
Moment of inertia and angular velocity are inversely proportional in order to conserve angular momentum.
This is an application of the angular analogue of Newton’s first law of motion
At the start the Diver initiates the somersault with feet on the
board. This means the body is extended and angular velocity is low.
At this point moment of inertia is high meaning rotation is low.
During the middle of the somersault the diver tucks tight reducing the moment of inertia and increasing angular velocity
