ProjectilesMotion in Two Dimensions

Chapter 7

Projectile An object launched into the air by a force

Trajectory The path followed by a projectile

Horizontal Motion

• The red ball moves horizontally at equal intervals (constant velocity)

• It is not speeding up or slowing down

Independence of Motion

• All the balls fall at the same rate

• The horizontal and vertical motions are independent of each other

Projectile Motion Equations

Objects Launched at an Angle

Range (R)• The horizontal distance traveled by a projectile

Velocity Components• Determine the vertical (y) and horizontal (x) components of the

initial velocity.

Projectiles at an Angle

• Then use the values in the original equations

Hang-Time equation

Should be negative 2

Maximum Height equation• Same equation as before• Time = ½ the total time• Why?

Range equation

• Horizontal distance• Same equation as

before• X = Vx t

7.2 Periodic Motion

• Repeating Motion• An object on a string• Pendulum• Bouncing on a spring

Circular Motion• Velocity is

perpendicular (tangent) to the radius

Centripetal Acceleration

• “Toward the center”• The rate of change of

tangential velocity

Period• Period (T) is the time of a complete revolution• 2 pie r = circumference = distance• Velocity = distance / time

Centripetal Acceleration Equation

Centripetal Forces• There must be a force to cause acceleration

Centripetal Force Equation• Newton’s second law

Changing Circular Motion: Torque

Simple Harmonic Motion

Amplitude

Pendulum• The period of the pendulum

depends only the length. NOT mass or amplitude

Pendulum• Can be used to calculate g at a specific location