Chapter 7 Motion in Two Dimensions
7.1 Projectile Motion
The path of a projectile is its trajectory.
Independence of Motion in Two Dimensions
The horizontal and vertical velocities of a projectile are independent.
Time is the only common factor.
Horizontal Component of Projectile Motion
dx = vxt
Vertical Component of Projectile Motion
dy = vy1t + ˝gt2
vy2 = vy1 + gt
vy22 = vy12 + 2gdy
Objects Launched Horizontally
The horizontal Velocity is constant.
The vertical velocity is constantly changing because of gravity.
Objects Launched at an Angle
The trajectory of a projectile is a parabola.
Problem Solving Strategy
Solve the horizontal and vertical components independently of each other.
Always check a problem to see if you answers are reasonable.
The velocity of a projectile can be resolved into horizontal and vertical components.
7.2 Periodic Motion
Circular Motion
Centripetal acceleration is always toward the center of a circle.
In circular motion, centripetal acceleration is at right angles to the instantaneous velocity.
ac = v2/r
Where:
a centripetal acceleration
v linear velocity, tangential to the circle.
r radius of the circle
v = (2pr)/T
where:
T period of one revolution
a = (4p2r)T2
Fc = mac = (mv2)/r = (4p2mr)/T2
Where:
Fc centripetal force
m mass of object
Changing Circular Motion: Torque
Torque is the product of the force and lever arm.
T = F X l
Simple Harmonic Motion
In simple harmonic motion, the restoring force varies linearly with displacement
The period is the time required to complete a full complete cycle.
A pendulum making small swing undergoes simple harmonic motion
Period of a Pendulum:
T = 2p(l/g)1/2
Where:
l length of pendulum
