Biomechanics • Mechanics of movement: – vectors and scalars – velocity, acceleration and momentum/impulse in sprinting – Newton’s Laws applied to movements – application of forces in sporting activities – projectile motion – factors affecting distance, vector components of parabolic flight – angular motion – conservation of angular momentum during flight, moment of inertia and its relationship with angular velocity.

Copy and label your diagram to show the changing vertical and horizontal vectors at the following points: - the point of release - the highest point of flight - the point immediately before landing. (3 marks) Point of release A. Positive vertical component Highest point B. No vertical component Before landing C. Negative vertical component D. Equal horizontal component at all three points in flight Vector arrows must be present and attached to the correct point on the parabolic curve

Angular Motion Angular motion is the movement of an object that is rotating – i.e. movement around an axis. We usually apply angular motion to athletes who are rotating such as a gymnast, ice skater or diver, although it can also be applied to rotating body parts such as in the long jump. Recap – AS PE: What were the names of the 3 axis of rotation, and where do they pass through the body?

Axis 1 2 3 1. Longitudinal axis… … e.g. full twisting jump. The body can rotate around 3 axis: 1 1. Longitudinal axis… … e.g. full twisting jump. 2. Frontal (Anterio-posterior) axis… … for lateral rotation (e.g. cartwheel) 3. Transverse axis… … for forward rotation (e.g forward roll) 2 3

Angular vs Linear Motion All of the key terms learnt about linear motion have angular counterparts, including: Angular Distance Angular Displacement Angular Speed Angular Velocity Angular Acceleration Torque / Moment Moment of Inertia Angular Momentum Leave space beneath to include def. for each

Angular Distance and Displacement Angular distance is… …the distance (angle) travelled by an object rotating around an axis It is measured in… degrees (˚) or radians (rads). Angular displacement is… …the smallest distance (angle) between starting and finishing positions

Radians The radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. As the circumference of a circle = 2πr = 360˚ 1 radian = 360 / 2π 1 rad = 57.3˚

Angular Velocity Angular velocity is… …the angle through which a body rotates about an axis in one second It is measured in… radians/sec Degrees must be converted into radians 2π radians = 360° 1 radian = 57.2953 ° 1 degree = 0.017453 radian

Angular Acceleration Angular acceleration is… …rate of change of angular velocity It is measured in… radians/sec2

Turning Moments, or Torque A moment or torque is the turning effect of a force. The size of the moment / torque depends upon the size of the force and the distance that the force acts from the axis of rotation (pivot) The standard measurement of a torque is Newton metres (Nm). All rotation must start with a torque. This occurs when a force acts outside the centre of mass of the body – this is called an eccentric force

Newton’s Laws of Angular Motion Basically the same as his laws on linear motion, except this time you’re talking about something that’s rotating!

Newton’s 1st Law of Angular Motion A rotating body will continue to turn about its axis of rotation with constant angular momentum unless an eccentric force is exerted upon it. This is also known as the ‘law of conservation of angular motion’

Newton’s 2nd Law of Angular Motion Newton’s 3rd Law of Angular Motion Angular acceleration is proportional to the torque (force) causing it and takes place in the direction in which the torque acts. Newton’s 3rd Law of Angular Motion For every torque that is exerted by one body on another, there is equal and opposite torque exerted by the second body on the first.

Moment of Inertia Moment of Inertia (MI) is… …the resistance of a body to change its state of rotational / angular motion It depends on two things: Mass – the more massive an object, the greater the MI Distribution of mass around the axis of rotation

Moment of inertia and mass

MI and Distance greater more Moment of inertia i.e. The further away its mass is away from the axis of rotation, the its moment of inertia and the force is required to make it spin or stop it spinning if rotation is already occurring. This can be simply depicted in the following graph: greater more Moment of inertia Distance of mass from axis

The Moment of Inertia (MI) can be calculated as follows: MI = Sum (mass of body x distance from axis part of rotation2 ) Or MI = Σ(mxr2) Any small difference in the distance of the mass from the axis has a big effect on MI If r doubles, MI increases If r increases four-fold, MI increases four times! 16 times!

Seeing it in practice

Angular Momentum NB/ Linear Momentum is calculated as: Mo = Angular momentum is calculated as the product of Moment of Inertia (MI) and angular velocity (ω) Angular Momentum = Mass x velocity MI x ω

Recap - Newton’s 1st Law of Angular Motion A rotating body will continue to turn about its axis of rotation with constant angular momentum unless an eccentric force is exerted upon it. This is also known as the ‘law of conservation of angular motion’ When an object is mid-flight, angular momentum must remain constant, unless an external force acts on the object.

When an object is mid-flight, angular momentum must remain constant, unless an external force acts on the object. As angular momentum = if, during that flight, MI increases, angular velocity must decrease, and vise versa. Therefore by reducing the size of the lever we increase the speed of the rotation. MI x ω (angular velocity),

The spinning chair experiment…

Application to sport – ice skating

Application to sport – trampoline

The relationship between angular momentum, moment of inertia and angular velocity are more commonly shown as a graph and diagram: What external factors will be acting on the diver once they have taken off from the board? According to Newton’s First Law of Angular Motion, what will happen to the angular momentum of the diver from the point of take off until landing? What happens to the Moment of Inertia (MI) as the diver changes from a straight to a pike position and back again? What therefore must happen to angular velocity during this change in body position (remember that Angular Momentum = MI x ω) Sketch lines on the graph to show Angular Momentum, Moment of Inertia and Angular Velocity. Increasing Value Time

Example exam question: Ice skating competitions involve skating programmes that last approximately five minutes, and may involve spinning movements that confrom to mechanical principles. The figure shows an ice skater performing part of Her routine. Q. Using the figure explain the mechanical principles that allow spinning ice skaters to adjust their rate of spin. (6)

(n.b. On diagrams mark annotations) Mark scheme: ice is a friction free surface. During rotations, angular momentum remains constant. Angular momentum = moment of inertia x angular velocity Angular momentum. Quantity of motion/rotation Moment of inertia. Spread/distribution of mass around axis/reluctance to rotate. Angular velocity = speed of rotation Change in moment of inertia leads to change in angular velocity/speed/spin of rotation. Brings arms/legs closer to/further away from axis of rotation/body leads to increase/decrease in angular velocity/speed of rotation/spin. (n.b. On diagrams mark annotations)