class 051107

Chapter 3:

121:  1-4, 9, 13, 17, 18, 22, 25

201:  1-5, 9, 12, 13, 16, 19, 20, 22, 25, 30, 33

Chapter 4

121: 1-4, 19-22, 25, 31, 36-39

201: 21, 23, 25, 26, 29, 31, 34, 39,44,47,49,55,58

Intro Prob Sets

Set 6, #5-6

Set 7, #11-12

Chapter 5

121: 1-4, 9, 28-29, 43, 44

201: 3, 6, 9, 14, 18, 26, 30, 31, 36, 40, 43, 46, 50

Chapter 7: 47, 48, 50

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Radian measure of angles

Semi-official definition: a 1 radian angle is an angle from the center of the circle defined by an arc distance equal to the radius.

The circumference of a circle is 2 pi r, approximately 6.28 r.

How many 1-radian angles will 'fit' around a circle?

Each 1-radian angle requires arc distance r.  The circumference is about 6.28 r.  So we're gonna be able to put about 6.28 arc distances of r around that circle.  Each one corresponds to a 1-radian angle.

We conclude that there are about 6.28 radians around the circle.

More precisely there are 2 pi radians around the circle.

How many degrees are there around that circle?

Everyone knows there are 360 deg around the circle.

How many degrees are there in a radian?

From the above, 360 deg is the same as 2 pi rad.  So we have

360 deg = 2 pi rad.

To get 1 rad we divide both sides by 2 pi:

360 deg / 2 pi = 2 pi rad / (2 pi) or

1 rad = 360 deg / (2 pi) = (180 / pi)  deg

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`T Change in velocity is represented by an area beneath an acceleration vs. clock time graph.
`F The area beneath a velocity vs. clock time trapezoid is (vf - v0) / `dt * 2.
`F Final velocity = initial velocity + change in acceleration.
`F The third equation of uniformly accelerated motion where velocity and position are regarded as functions of clock time is x = x0 + v0 t + 1/2 a `ds.
`F If we know two of the four quantities v0, vf, `ds and `dv for a freely falling object then we can find the other two.
`F For an ideal projectile whose initial vertical velocity is zero, if we know any of the three quantities vf_x, `ds_x, `dt we can use the equations of motion to find the values of the other two.
`F An Atwood machine is set up so that when the greater mass descends the motion is in the clockwise direction. The counterclockwise direction is generally taken to be the positive direction for rotation, and that will be the case here. If the lesser mass is descending then the velocity is positive while the acceleration is positive.
`T If an object moves with changing speed along a uniform incline then its acceleration parallel to the incline is nonzero.
`F If an object moves with changing speed along a uniform incline then the net force parallel to the incline is zero.
`F An Atwood machine is set up so that when the greater mass descends the motion is in the counterclockwise direction, which is taken to be the positive direction for rotation. The system is given an initial velocity in the clockwise direction. The net force acting on this system is negative.
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`F The definition of average velocity is the rate of change of acceleration with respect to clock time.
`T Change in position is represented by an area beneath a velocity vs. clock time graph.
`T Change in velocity is represented by an area beneath an acceleration vs. clock time graph.
`F The area beneath a velocity vs. clock time trapezoid is (vf - v0) / `dt * 2.
`F Average velocity is the average slope of an acceleration vs. t graph.
`F Final velocity = initial velocity + change in acceleration.
`T The second equation of uniformly accelerated motion where velocity and position are regarded as functions of clock time is v = v0 + a t.
`F If we know two of the four quantities v0, vf, `ds and `dv for a freely falling object then we can find the other two.
`F For an ideal projectile whose initial vertical velocity is zero, if we know any of the three quantities vf_x, `ds_x, `dt we can use the equations of motion to find the values of the other two.
`T If we choose the downward direction as positive then if a ball is thrown upward its initial velocity is negative and its acceleration is positive.
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`F The definition of average velocity is the rate of change of acceleration with respect to clock time.
`T If acceleration is uniform then the velocity vs. clock time graph is a straight line.
`F The first equation of uniformly accelerated motion on an interval is `ds = (vf - v0) / 2 * `dt.
`T The second equation of uniformly accelerated motion where velocity and position are regarded as functions of clock time is v = v0 + a t.
`T If the acceleration of an object is in the direction direction opposite its velocity then the object slows down.
`T For an ideal projectile whose initial vertical velocity is zero, if we know the vertical displacement and horizontal range then we can find the initial horizontal velocity.
`T If we choose down an incline as positive then an object coasting down the incline has a positive initial velocity.
`F An Atwood machine is set up so that when the greater mass descends the motion is in the counterclockwise direction, which is generally taken to be the positive direction for rotation, and that will be the case here. If the lesser mass is descending then the velocity is positive while the acceleration is positive.
`F If an object is moving in the negative direction and and its acceleration is in the positive direction then it is speeding up.
`T If an object slides or rolls from rest down an incline under the influence of only friction, gravity, and the bending or compressive response of the incline to the gravitational force, then the net force perpendicular to the incline is zero.
84348.8
`T Change in position is represented by an area beneath a velocity vs. clock time graph.
`F If (vf + v0) / 2 is not equal to vAve then the position vs. t graph is not a straight line.
`T The fourth equation of uniformly acceleration motion on an interval is vf^2 = v0^2 + 2 a `ds.
`F For an ideal projectile the vertical motion is characterized by the quantities v0_y, vf_y, `ds_y, `dt_y and acceleration equal to the downward acceleration zero.
`F For an ideal projectile the horizontal motion is characterized by the quantities v0_x, vf_x, `ds_x, `dt_x and acceleration equal to the acceleration of gravity.
`F For an ideal projectile the horizontal acceleration is 980 cm/s^2, so that the average horizontal velocity `ds_x / `dt is not equal to the initial or the final horizontal velocity.
`T If we choose the downward direction as positive then if a ball is thrown upward its initial velocity is negative and its acceleration is positive.
`F If we choose the upward direction as positive then if a ball is thrown upward its initial velocity is positive and its acceleration is positive.
`F Newton's First Law says that an object remains in its state of rest or uniform velocity in a straight line only if no forces act on the object.
`T Newton's third law says that if one object exerts a force on the other, the other exerts and equal and opposite force on it.