# PH.5 a-d - Linear, Circular, and Projectile Motion

The student will investigate and understand the interrelationships among mass, distance, force, and time through mathematical and experimental processes. Key concepts include

a)  linear motion;

b)  uniform circular motion;

c)  projectile motion;

d)  Newton’s laws of motion;

Bloom's Levels:  Analyze; Understand

### BIG IDEAS

• I can determine how long it would take me to walk to the mall.
• I can explain why roller coasters don't fall off the track when they go upside down.
• I can explain how rockets work.
• I can explain why I get "thrown" to one side in the car on a sharp turn.

### UNDERSTANDING THE STANDARD

The concepts developed in this standard include the following:

• Newton’s three laws of motion are the basis for understanding the mechanical universe.
• Linear motion graphs include
• displacement (d) vs. time (t)
• velocity (v) vs. time (t)
• acceleration (a) vs. time (t)
• Position, displacement, velocity, and acceleration are vector quantities.
• Motion is described in terms of position, displacement, time, velocity, and acceleration.
• Velocity is the change in displacement divided by the change in time. A straight-line, position-time graph indicates constant velocity. The slope of a displacement-time graph is the velocity.
• Forces are interactions that can cause objects to accelerate. When one object exerts a force on a second object, the second exerts a force on the first that is equal in magnitude but opposite in direction.
• An object with no net force acting on it is stationary or moves with constant velocity.
• Acceleration is the change in velocity divided by the change in time. A straight-line, velocity-time graph indicates constant acceleration. A horizontal-line, velocity-time graph indicates zero acceleration. The slope of a velocity-time graph is the acceleration.
• The acceleration of a body is directly proportional to the net force on it and inversely proportional to its mass.
• In a uniform vertical gravitational field with negligible air resistance, horizontal and vertical components of the motion of a projectile are independent of one another with constant horizontal velocity and constant vertical acceleration.
• An object moving along a circular path with a constant speed experiences an acceleration directed toward the center of the circle.
• The force that causes an object to move in a circular path is directed centripetally, toward the center of the circle.  The object’s inertia is sometimes falsely characterized as a centrifugal or outward-directed force.

### ESSENTIALS

In order to meet this standard, it is expected that students will

a) construct and analyze displacement (d) vs. time (t), velocity (v) vs. time (t), and acceleration (a) vs. time (t) graphs.

solve problems involving displacement, velocity, acceleration, and time in one and two dimensions (only constant acceleration).

b) distinguish between centripetal and centrifugal force.

describe the forces involved in circular motion.

c) resolve vector diagrams involving displacement and velocity into their components along perpendicular axes.

draw vector diagrams of a projectile’s motion. Find range, trajectory, height of the projectile, and time of flight (uniform gravitational field, no air resistance).

solve problems related to free-falling objects, including 2-D motion.

d) solve problems involving force (F), mass (m), and acceleration (a).

solve problems involving multiple forces, using free-body diagrams.

### KEY VOCABULARY

Updated: Dec 01, 2017