Understanding Projectile Motion

Projectile Motion

• A projectile is any object projected into the air that moves freely, without its own power source, such as a netball, a cricket ball hit for six, or an aerial skier
• These objects follow smooth, parabolic paths due to free fall
• Free fall occurs once the projectile releases, where the forward force ceases, and gravity is the only force acting on the ball
• Downward direction is positive when discussing projectile motion

Projectile Under Free Fall

• At the moment of release, the initial vertical velocity is zero
• In the vertical direction, the projectile experiences constant acceleration at 9.8 m/s²
• Projectile launches horizontally possess an initial horizontal velocity only, with zero initial vertical velocity.
• The initial horizontal speed dictates velocity's horizontal component throughout the flight
• The distance traveled is equal to the displacement's magnitude
• The actual speed, v, after finding horizontal (vx) and vertical (vy) can be calculated using Pythagoras’ theorem

Projectiles Launched Obliquely

• Separation and independent treatment, involving vertical and horizontal motion components, is needed
• Calculate initial velocity for vertical and horizontal components via trigonometry
• Horizontal motion exhibits constant velocity (vx=ux, ax=0)
• Vertical motion has constant acceleration (a=9.8 m/s²), with velocity decreasing as the projectile rises, reaching vy=0 at the top, then increasing as it descends

Initial Conditions

• Complementary launch angles yield the same horizontal distance
• Increasing the launch angle above 45° increases the height, and complementary angles(30° ,60°) give range with varying heights/times of flight.
• Rising initial velocity enhances the projectile's maximum height and range
• The horizontal velocity component mainly influences range, as the vertical part impacts maximum height and flight time
• Height increase relates to higher launch points to get a greater time of flight as well horizontal range

Circular Motion

• Characterized by objects moving in a circular path with a constant speed but with continually changing velocity

Uniform Circular Motion

• While velocity changes, the hammer’s speed remains constant, such as in a hammer thrower
• A hammer's velocity at one instant may be 25 m/s north, and seconds later, west, then south
• This constant velocity indicates acceleration

Period and Frequency

• The time (T) required for one complete revolution when being constant speed, v, and radiu is r.
• The number of rotations per second is frequency, f
• Period = time/no.revolutions

Speed

• Revolutions have a distance equal to the circle's circumference, C = 2πr
• Average object speed: speed = distance / time
• Calculations calculate speed: 2πr/T

Calculating Speed

• Frequency is measured in Hertz
• 20 revolutions in 60 s means that each revolution (T) takes 3 s

Angular Velocity

• Used to measure angle rotation over time, such as Θ/r in rad

Centripetal Acceleration

• Shows velocity causes acceleration when a speed remains constant
• Motion shows continual inward movement deviating from its straight path
• Acceleration to the motion's direction

Forces and Circular Motion

• Force gives the direction of acceleration toward the circle's center
• Tension in cable example would include the release of the hammer

Banked Tracks

• Normal force becomes gravitational attraction to the central body for a car on a curved, tire friction
• Tension in a straight path goes together with its centripetal acceleration
• Circular motion happens on banked and inclined corners peaking at 42°, cyclists can travel at higher speeds

Ball on String

• Slow, string has a downward swing
• Fast, sting turns horizontal
• The angle helps determines the radius and involved forces

Object on a string

• This uses trigonometry, two forces, and unbalanced forces
• The ball towards center indicates force triangle trigonometry

Banked Corners

• Horizontal roads are for tyre friction which also keep the circular path
• The net forces are a steady speed clockwise
• Acceleration is towards the circle's enter, as the forces, gravity
• Horizontal sideways balances the normal reaction, a car without friction skids at circular path banking
• Sideways friction and speeding are on reduced and banked road
• Friction depends to an angle which is not affected

Work and Energy

• Constant speed shows circular path for similar vertical paths/rollercoasters
• Experience quite strong forces pushing you down into the seat
• High and fly through the dips of the sea

Uniform Horizontal Motion

• Normal reaction helps normal force
• Force bounces upon normal reaction
• Circular motion is with, force is a celerity when equal of apparent weight

Conservation of Mechanical Energy

• Conserved by potential and kinetic transformation into heat, light, and viscous versa
• Spacecraft dissipate kinetic during reentry, or shooting stars from Meteors happens because of heat generated by friction.

Vertical Circular Motion

• Determine final/bottom ramp by moving with kinetic and potential
• Acceleration upward provides net potential and requires some upwards reaction
• Coasters provides the centripetal reaction vertically

Work in Joules

• Transformations occurs in separate force parallel
• Actions creates object perpendicularly

Torque

• Pivots have force while rotating.

What Newtons show

• Newtons are a gravitational show because planets have orbit
• A gravitational pulls the Earth and the moon by affecting a sphere
• Earth and moons moves all matter to its sides
• A sphere indicates uniform
• Satellite allows Newton to be balance out

Satellites

• Constant speed allows satellites to be circular in orbit while the area is being parallel