Phys 270- 3: Motion In Two Or Three Dimensions

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Displacement:

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the change in position

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position vector:

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Average Velocity:

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Instantaneous Velocity:

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the limit of the average velocity as the time interval approaches zero, and it equals the instantaneous rate of change of position with time.

- magnitude of the vector at any instant is the speed of the particle at that instant

- direction of the vector at any instant is the same as the direction in which the particle is moving at that instant.

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magnitude of instantaneous velocity:

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the speed

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What does acceleration describe?

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how the velocity of the particle changes.

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Average Acceleration:

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during time interval as the velocity change divided by the time interval.

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Instantaneous acceleration:

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the limit of the average acceleration when point 2 approaches point 1 and the change in velocity and change in time approach zero.

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The acceleration vector can be described:

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- changes in the particle's speed

- its direction of motion

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Projectile:

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any body that is given an initial velocity and then follows a path determined entirely by the effects of gravitational acceleration and air resistance.

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trajectory:

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the path followed by projectile.

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key to analyzing projectile motion:

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we can treat the x and y coordinates separately.

- x component of acceleration = 0

- y component of acceleration is constant = -g

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projectile diagram:

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representing initial velocity by its magnitude and direction:

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equations describing the position and velocity of the projectile at any time:

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Projectile's speed at any time:

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equation representing trajectory's shape in terms of x and y:

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Problem solving strategy 3.1: Projectile Motion:

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Problem solving strategy 3.1: Projectile Motion:

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Motion in a circle:

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Uniform Circular Motion:

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the motion of a particle moving in a circle with constant speed.

- acceleration vector is perpendicular (normal) to the path and therefore directed inward (never outward) toward the center of the circular path...... [ causes the direction of the velocity to change without changing the speed]

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acceleration and velocity for a particle in uniform circular motion and for a projectile with no air resistance.

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equation for the speed of a particle traveling around a circle:

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another equation for uniform circular motion:

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Centripetal acceleration:

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the acceleration directed toward the center of the circle

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period (T):

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- another way to express magnitude of acceleration in uniform circular motion.

- the time for one revolution (one complete trip around the circle).

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Nonuniform circular motion:

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Relative velocity:

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the velocity seen by a particular observer... called the velocity relative to that observer

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frame of reference:

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a coordinate system plus a time scale.

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In general, if A and B are any two points of frames of reference:

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Problem Solving Strategy 3.2: Relative Velocity:

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Galilean Velocity transformation:

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relates the velocity of a body P with respect to frame A and its velocity with respect to frame B

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Galilean Velocity transformation:

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relates the velocity of a body P with respect to frame A and its velocity with respect to frame B

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Summary:

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