B.2.1 Newton's Laws of Motion

Adapted from class notes.

Newton’s Laws

• Newton’s laws are the primary governing laws of classical physics that determine the general movement of objects through space

• Force, Power, Velocity, and energy are specifically defined terms

Kinematics

• Kinematics is the study of motion

• Motion can be:

  • Linear - In one-dimensional space (someone running, a ball rolling)

  • Curvilinear - In two-dimensional space, up/down AND forward/back (a ball thrown)

  • Angular - Around an axis in a circular motion (a lever, or a gymnast on a bar)

  • General - Some combination of linear and angular

Measurements and Position

• Scalar vs. Vector

  • Vector - A measurement with a size and direction (10 m/s north)

    • Direction matters! 10 m/s + 10 m/s doesn’t always equal 20 m/s, it could be 0 because the directions cancel out (10 m/s left + 10 m/s right), or anything in between taking angles into consideration

  • Scalar - A measurement with a size but not direction (10 kg)

• Position - Measured with coordinates, a measure of distance from some origin along two or three axes (horizontal, vertical, lateral)

Linear - Displacement/Distance

• Distance - How far an object has traveled. Path matters! Symbol is typically “d”

• Displacement - How far from the origin. Path does not matter. Symbol is typically “s”

• Ex. I walk to my friend’s house. In a straight line, that is 2 km away. But I wander a bit, and end up walking 5km. My displacement is 2km, but I traveled 5km

Linear - Velocity

• Velocity - Change in displacement over time with size and direction (vector)

  • v = s/t

• Speed is the size of the velocity, but without direction (scalar)

• Units are m/s or ms-1

• Ex. I run a 100m race in 20 seconds. Best time! I had an average velocity of 100m/20s = 5 m/s. This means that I moved about 5 meters every 1 second

Linear - Acceleration

• Acceleration - Change in velocity over time with size and direction (vector)

  • a - v/t = (v-u)/t when v is final velocity and u is initial velocity

• Units are m/s/s or ms-2

• Ex. The beginning of my 100m race I started from stop, and reached a maximum velocity of 6 m/s in 3 seconds. During this time I accelerated at 2 m/s/s. Meaning that every second, my velocity increased by 2 m/s

Angular Kinematics

• Deals with rotation around an axis (like a joint)

• Examples of rotation in sports/exercise

  • A spinning ball pitched in baseball

  • A flip turn in swimming

  • A golf club swinging

  • A gymnast spinning on the uneven bars

  • A dancer twirling

  • A cartwheel

  • Many joint movements (bicep curls for example)

Angular - Displacement and Velocity

• Angular displacement is the angular movement around an axis. Symbols is theta. Measured ind egrees or radians

  • Flexing the elbow would yield a displacement ~150 degrees (depending on ROM)

• Angular velocity is the rate at which angular displacement happens. Represented with the letter omega. Measured in degrees/s, degrees s-1, rad/s, rads-1

  • Omega = theta/t but also, v = omega times r where r is the radius of the circle made by some object moving with the angular velocity of omega (in rad/s) and v is the linear velocity (in m/s) that it would be moving

  • Also can be represented as v = 2pir/T where r is the radius and T is the time it takes to complete the circle

• Example - A bicep curl is performed. The angular displacement in 150 degrees. The length of the forearm from elbow to weight in hand is 30cm. If the bicep curl takes 0.5 seconds to complete, the angular velocity is 300 degree/s or 5pi/3 rad/s, and the weight held in the hand moves at 157 cm/s

Angular - Acceleration

• Angular acceleration represented with the Greke letter a, alpha

• Units are degrees/s/s, degrees s-2, rad/s/s, or rad s-2

• /s/s can also be represented as /s2

• Has direction (vector)

Instantaneous vs Average

• Instantaneous refers to the measurement at any one point in time

• Average regers to the overall measurement

• Ex. If I run a 100m dash, I start from stop. This means that I will accelerate for a few seconds to my maximum velocity. If it takes me 20 seconds to run this, I had an average velocity of 5m/s, but because I accelerated at the start, there were periods in the beginning of my race that had instantaneous velocities lower than 5m/s, and toward the middle and end of my race that were greater than 5 m/s

• Additionally, during the first 3 seconds, I had instantaneous acceleration of 2ms-2, but when averaged with the end of the race (where I slowed down) the average acceleration is only 0.5m s-2

Kinetics

• Kinetics involve the forces acting on objects

• Force: A mechanical interaction between two objects involving contact or no contect (as in gravity)

• Resultant motion: The motion becayse of all the forces acting on an object

• Gravity: An attractive force between all objects with mass

• Mass: The amount of material

• Weight: The effect of gravity on mass

Newton’s Laws: First

1. Alternate Name

2. Description

1. Law of Inertia

2. An object at rest stays at rest, or an object in motion stays in motion UNLESS acted on by a force. Inertia is resistance to change in movement

Newton’s Laws: Second

1. Alternate Name

2. Description

1. Law of Acceleration

2. The acceleration of an object is proportional to the force acting on it, and inversely related to its mass. F = m times a, Fg = m times g, F = m(Vf - Vi)/t

Newton’s Laws: Third

1. Alternate Name

2. Description

1. Law of Reaction

2. For every action there is an equal and opposite reaction. Forces are the same, but results might not be the same

Application of Newton’s Laws

• Principle of Stability - Stability is affected by:

  • The height of the center of mass (lower is more stable)

  • Large base of support is more stable

  • Line of gravity (horizontal center of mass) above base of support is more stable

  • Greater mass is more stable

• Principle of summing joint forces - Multiple forces may act on any joints, the overall movement is the sum of the forces. If forces at in same direction, they add

• Principle of linear momentum and linear impulse:

  • Linear momentum is the amount of movement, p = m times v (momentum is mass times velocity)

  • Linear impulse is time that a force acts, J = F times N, linear impulse is the change in momentum

  • Large forces acting for a long time results in a large change in momentum (velocity)

• Principle of impulse direction - The direction of the applied force translates to change in momentum toward that direction. A stopped object will move in that direction. A moving object will shift toward that direction (but might not entirely move that way)

Application of Newton’s Laws: Principles of Angular Movement

• Torque - A force causing rotation. Torque depends on the size of the force, the distance the force is from rotational axis, and the angle which it is applied. T = F times d times sintheta. Big force, large distance, or a perpendicular angle of force creates the largest torque

• Moment of inertia - A measure of difficulty of an object to rotate. A large moment of inertia is hard to rotate. When the center of mass of the rotating object is far from the axis, it will have a difficult time rotating. Also affected by shape of an object. Measured in kg m-2

• Angular momentum - the amount of rotation. Measured in kg m s-1. Represented by “L”. L = I times omega (moment of inertia times angular velocity). Generated in the body through muscle contraction

• Conservation of angular momentum - An angular version of the first law. Rotation will continue unless acted on by a force, or won’t begin until acted on. When a person is rotating (as in diving, or in gymnastics), they can change their shape, which would change their moment of inertia. To maintain angular momentum, their angular velocity would change. This is how divers/gymnasts can perform various flips easier in some positions than others

• Trading angular momentum - As an object is spinning, if a body changes its shape to have greater angular velocity on one side, then the rotation can be transferred to a different axis. Meaning a flip can turn into a spin through changing body position