Podcast
Questions and Answers
Why must the descriptions of motion be extended to two- and three-dimensional situations?
Why must the descriptions of motion be extended to two- and three-dimensional situations?
- To simplify the calculations of motion.
- Because all objects move in straight lines.
- Because objects do not always move in a single line. (correct)
- To avoid using vector quantities.
What is the definition of the position vector of a particle at an instant?
What is the definition of the position vector of a particle at an instant?
- A vector representing the particle's acceleration.
- A vector tangent to the particle's path.
- A vector that goes from the origin to the particle's location. (correct)
- A scalar that indicates the particle's speed.
The average velocity vector always points in the same direction as which of the following?
The average velocity vector always points in the same direction as which of the following?
- The displacement vector. (correct)
- The final position vector.
- The acceleration vector.
- The initial position vector.
The instantaneous velocity vector is always what to the path of a projectile?
The instantaneous velocity vector is always what to the path of a projectile?
What represents the speed of a projectile?
What represents the speed of a projectile?
What is the relationship between a particle's velocity components and its coordinates?
What is the relationship between a particle's velocity components and its coordinates?
If a particle is moving in the xy-plane, what must be true of z and (v_z)?
If a particle is moving in the xy-plane, what must be true of z and (v_z)?
What does the instantaneous acceleration vector describe?
What does the instantaneous acceleration vector describe?
If the direction of a car's acceleration is opposite to the acceleration, what will occcur?
If the direction of a car's acceleration is opposite to the acceleration, what will occcur?
The velocity vector is always tangent to which of the following?
The velocity vector is always tangent to which of the following?
Which statement is correct concerning instantaneous acceleration and average acceleration?
Which statement is correct concerning instantaneous acceleration and average acceleration?
A particle is moving along a curved path. When is the acceleration tangent to this path?
A particle is moving along a curved path. When is the acceleration tangent to this path?
If a particle is moving in a curved path, which direction does the acceleration vector point?
If a particle is moving in a curved path, which direction does the acceleration vector point?
Given that (a_{\parallel}) is the component of the acceleration parallel to a particle's velocity and (a_{\perp}) is the component perpendicular to the velocity, what do these components tell us?
Given that (a_{\parallel}) is the component of the acceleration parallel to a particle's velocity and (a_{\perp}) is the component perpendicular to the velocity, what do these components tell us?
When an object is turning, what must be true about its acceleration and velocity?
When an object is turning, what must be true about its acceleration and velocity?
The equation is given: $y = (tan \alpha_0)x - \frac{g}{2(v_0 cos \alpha_0)^2}x^2$. This refers to which of the following?
The equation is given: $y = (tan \alpha_0)x - \frac{g}{2(v_0 cos \alpha_0)^2}x^2$. This refers to which of the following?
If you want to achieve the maximum range for a projectile, what launch to you use?
If you want to achieve the maximum range for a projectile, what launch to you use?
While a projectile is in motion, what statements are true?
While a projectile is in motion, what statements are true?
How you can calculate the projectile coordinate as a function of time?
How you can calculate the projectile coordinate as a function of time?
What is the value of ax and ay respectively while the projectile is in flight?
What is the value of ax and ay respectively while the projectile is in flight?
At which point is the projectile on a trajectory if the following conditions are satisfied: uy = 0, the particle still exists, still possesses kinetic energy, gravity still exists
At which point is the projectile on a trajectory if the following conditions are satisfied: uy = 0, the particle still exists, still possesses kinetic energy, gravity still exists
Which best describes uniform circular motion?
Which best describes uniform circular motion?
An object has a period, denoted T. How is the object's magnitude acceleration related to the radius of the object?
An object has a period, denoted T. How is the object's magnitude acceleration related to the radius of the object?
Which statement about the difference between circular and projectile motion is correct?
Which statement about the difference between circular and projectile motion is correct?
Assuming that an object goes around a loop, which statement is guaranteed to be true?
Assuming that an object goes around a loop, which statement is guaranteed to be true?
If relative velocity is important, which one of the following needs to be true?
If relative velocity is important, which one of the following needs to be true?
Which of the following describes the expression, UP/A-x = UP/B-x + UB/A-x?
Which of the following describes the expression, UP/A-x = UP/B-x + UB/A-x?
Why does the statement below need to be solved to derive an efficient problem setup? 'The known u(T/E) is an actual and rearranges: UT/E-x = UT/Y-x + UY/E-x'
Why does the statement below need to be solved to derive an efficient problem setup? 'The known u(T/E) is an actual and rearranges: UT/E-x = UT/Y-x + UY/E-x'
If A and B frame of reference, then which of the following statements is true?
If A and B frame of reference, then which of the following statements is true?
If you are told to solve for 2 unknowns during an equation, but it requires 3 dimensions, what can you do?
If you are told to solve for 2 unknowns during an equation, but it requires 3 dimensions, what can you do?
In projectile motion, what is the purpose of setting (y = 0)?
In projectile motion, what is the purpose of setting (y = 0)?
A tranquilizer dart having relatively low muzzle velocity reaches point P before touching the monkey. In this case assuming drag has been accounted for, what location will the monkey be?
A tranquilizer dart having relatively low muzzle velocity reaches point P before touching the monkey. In this case assuming drag has been accounted for, what location will the monkey be?
A and B refer to which of the following?
A and B refer to which of the following?
What is the Galilean transformation?
What is the Galilean transformation?
At high speeds near c, what is the value of calculating the Galilean relativity with the train and speed, assuming the train moves at c to the same direction?
At high speeds near c, what is the value of calculating the Galilean relativity with the train and speed, assuming the train moves at c to the same direction?
If a plane goes to 20 degrees west of north at what point would it be heading?
If a plane goes to 20 degrees west of north at what point would it be heading?
If the value airspeed indicator is 100km per second at -30 degrees from the starting point. Which statement is correct?
If the value airspeed indicator is 100km per second at -30 degrees from the starting point. Which statement is correct?
When solving for the magnitude and or the direction of a vector, which of the following is true?
When solving for the magnitude and or the direction of a vector, which of the following is true?
An artillery shell is fired, and one wishes to maximize the range with the same shell. If the same cannon is fired on that same shell underwater at 1000 atm of pressure, the range the shell travels is best described by which one of the following statements (assume cannon survives)?
An artillery shell is fired, and one wishes to maximize the range with the same shell. If the same cannon is fired on that same shell underwater at 1000 atm of pressure, the range the shell travels is best described by which one of the following statements (assume cannon survives)?
Flashcards
Position Vector
Position Vector
Vector that goes from the origin to the particle's location.
Average Velocity (vav)
Average Velocity (vav)
Displacement divided by the time interval.
Instantaneous Velocity (v)
Instantaneous Velocity (v)
Instantaneous rate of change of position with time; vector.
Velocity
Velocity
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Instantaneous Acceleration (a)
Instantaneous Acceleration (a)
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Parallel Acceleration (a||)
Parallel Acceleration (a||)
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Perpendicular Acceleration (a┴)
Perpendicular Acceleration (a┴)
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Projectile
Projectile
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Trajectory
Trajectory
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Projectile Motion
Projectile Motion
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Horizontal Distance
Horizontal Distance
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Uniform Circular Motion
Uniform Circular Motion
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Radial Acceleration (arad)
Radial Acceleration (arad)
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Nonuniform Circular Motion
Nonuniform Circular Motion
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Tangential Component(atan)
Tangential Component(atan)
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Relative velocity
Relative velocity
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Frame of Reference
Frame of Reference
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Study Notes
- Chapter 3 discusses motion in two or three dimensions, extending concepts from one-dimensional motion analysis.
- Includes describing motion with vector quantities like displacement, velocity, and acceleration in 2D and 3D space.
Position and Velocity Vectors
- The position vector pinpoints a particle's location in space relative to the coordinate system's origin.
- Represented as ŕ = xî + yĵ + zk, using Cartesian coordinates, where x, y, and z are vector components.
- Displacement is the change in position (∆ř) and is calculated as ∆ř = ř₂ - ř₁.
- Average velocity ( vav) is displacement over a time interval: vav = ∆ř / ∆t.
- Instantaneous velocity (v) is the limit of average velocity as the time interval approaches zero, v = lim(∆t→0) ∆ř / ∆t = dŕ/dt.
Vector Facts
- Instantaneous velocity direction is tangent to the particle’s path.
- Components of instantaneous velocity are the time derivatives of the coordinates: vx = dx/dt, vy = dy/dt, vz = dz/dt.
- Magnitude of instantaneous velocity (speed) is calculated using the Pythagorean theorem: v = √(vx² + vy² + vz²).
Acceleration Vector
- Acceleration describes changes in velocity, including both speed and direction.
- Average acceleration (av) is the change in velocity over a time interval: aav = ∆v / ∆t.
- Instantaneous acceleration (a) is the limit of the average acceleration as the time interval approaches zero: a = lim(∆t→0) ∆v / ∆t = dv/dt.
- Direction need not be tangent to the path. Points toward the concave side for curved paths.
- Components are the time derivatives of velocity components: ax = dvx/dt, ay = dvy/dt, az = dvz/dt or can be expressed, ax = d²x/dt², ay = d²y/dt², az = d²z/dt².
- Acceleration can be divided into components parallel (a||) and perpendicular (a┴) to the path. a|| affects speed and a┴ affects direction.
Projectile Motion
- Projectile motion involves objects launched into the air, affected by gravity and, in simplified models, neglecting air resistance.
- Trajectory lies in a vertical plane that is determined by the initial velocity vector.
- Treat horizontal and vertical motions separately.
- Horizontal motion has constant velocity (ax = 0), U x = Vox , x = xo + Voxt.
- Vertical motion has constant acceleration (ay= -g), Uy = Uoy, y = yo + Uoyt - gt2.
- Equations (3.19) to (3.22) describe position and velocity at any time t, assuming initial position as the origin.
- Trajectory shape in projectile motion can be expressed y = (tanα₀)x - (g / 2(vo cosα₀)²)x² which is a parabolic path.
More facts about projectile motion
- Maximum height reached is when vertical velocity component equals zero.
- Horizontal range (R) is greatest at a launch angle of 45 degrees = (vo² sin 2α₀) / g - (only when the launch and landing are equal).
Uniform Circular Motion
- Uniform circular motion occurs. A particle moves with constant speed in a circle.
- Acceleration is always directed toward the circle's center with magnitude: arad = v²/R. Radial is toward the center.
- Acceleration rewritten in terms of period (T): arad = 4π²R / T².
- Tangential acceleration (a) is zero since speed is constant.
Nonuniform circular motions
- Nonuniform circular motion occurs when speed changes
- Radial component is still arad = v²/R
- Tangential component atan = dv/dt and affects change in speed
Relative Motion
- Describes how motion appears to different observers in different reference frames.
- UP/A is P's velocity relative to frame A, *UP/B.
- Transformation equation: UP/A = UP/B + UB/A.
- Relative velocity equation relies on vector addition.
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