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
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