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Relationship between angle of banked road and normal force and its component
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$begingroup$
Why are these two angles in the diagram below equal? I can't quite see their relationship or proof of why they are the same.
kinematics
asked Mar 11 at 10:35
Max604Max604
312
$endgroup$
migrated from physics.stackexchange.com Mar 12 at 8:22
This question came from our site for active researchers, academics and students of physics.
add a comment |
$begingroup$
Why are these two angles in the diagram below equal? I can't quite see their relationship or proof of why they are the same.
kinematics
asked Mar 11 at 10:35
Max604Max604
312
$endgroup$
migrated from physics.stackexchange.com Mar 12 at 8:22
This question came from our site for active researchers, academics and students of physics.
1
$begingroup$
This is a plane geometry problem.
$endgroup$
– user45664
Mar 11 at 20:17
add a comment |
$begingroup$
Why are these two angles in the diagram below equal? I can't quite see their relationship or proof of why they are the same.
kinematics
asked Mar 11 at 10:35
Max604Max604
312
$endgroup$
Why are these two angles in the diagram below equal? I can't quite see their relationship or proof of why they are the same.
kinematics
kinematics
asked Mar 11 at 10:35
Max604Max604
312
asked Mar 11 at 10:35
Max604Max604
312
asked Mar 11 at 10:35
Max604Max604
312
asked Mar 11 at 10:35
Max604Max604
312
asked Mar 11 at 10:35
Max604Max604
312
312
migrated from physics.stackexchange.com Mar 12 at 8:22
This question came from our site for active researchers, academics and students of physics.
migrated from physics.stackexchange.com Mar 12 at 8:22
This question came from our site for active researchers, academics and students of physics.
1
$begingroup$
This is a plane geometry problem.
$endgroup$
– user45664
Mar 11 at 20:17
add a comment |
1
$begingroup$
This is a plane geometry problem.
$endgroup$
– user45664
Mar 11 at 20:17
1
1
$begingroup$
This is a plane geometry problem.
$endgroup$
– user45664
Mar 11 at 20:17
$begingroup$
This is a plane geometry problem.
$endgroup$
– user45664
Mar 11 at 20:17
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
On flat ground, $N$ points straight up.
Now, tilt the ground. For $N$ to remain perpendicular to the ground, it must "tilt along" - it must as well be tilted equally much. Tilt the ground with $theta$, and $N$ must as well tilt with $theta$ in the same rotational direction (clockwise in your case).
Otherwise, if it was tilted with any other angle, it wouldn't be perpendicular anymore.
answered Mar 11 at 10:40
SteevenSteeven
3751315
$endgroup$
add a comment |
$begingroup$
The angle between $f$ and the $x$-axis is equal to $theta$ because they are both complementary to the angle between $N$ and the $x$-axis. The angle in the fourth quadrant is equal to $theta$ because alternate interior angles are equal.
answered Mar 12 at 8:43
John DoumaJohn Douma
5,59711419
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
On flat ground, $N$ points straight up.
Now, tilt the ground. For $N$ to remain perpendicular to the ground, it must "tilt along" - it must as well be tilted equally much. Tilt the ground with $theta$, and $N$ must as well tilt with $theta$ in the same rotational direction (clockwise in your case).
Otherwise, if it was tilted with any other angle, it wouldn't be perpendicular anymore.
answered Mar 11 at 10:40
SteevenSteeven
3751315
$endgroup$
add a comment |
$begingroup$
On flat ground, $N$ points straight up.
Now, tilt the ground. For $N$ to remain perpendicular to the ground, it must "tilt along" - it must as well be tilted equally much. Tilt the ground with $theta$, and $N$ must as well tilt with $theta$ in the same rotational direction (clockwise in your case).
Otherwise, if it was tilted with any other angle, it wouldn't be perpendicular anymore.
answered Mar 11 at 10:40
SteevenSteeven
3751315
$endgroup$
add a comment |
$begingroup$
On flat ground, $N$ points straight up.
Now, tilt the ground. For $N$ to remain perpendicular to the ground, it must "tilt along" - it must as well be tilted equally much. Tilt the ground with $theta$, and $N$ must as well tilt with $theta$ in the same rotational direction (clockwise in your case).
Otherwise, if it was tilted with any other angle, it wouldn't be perpendicular anymore.
answered Mar 11 at 10:40
SteevenSteeven
3751315
$endgroup$
On flat ground, $N$ points straight up.
Now, tilt the ground. For $N$ to remain perpendicular to the ground, it must "tilt along" - it must as well be tilted equally much. Tilt the ground with $theta$, and $N$ must as well tilt with $theta$ in the same rotational direction (clockwise in your case).
Otherwise, if it was tilted with any other angle, it wouldn't be perpendicular anymore.
answered Mar 11 at 10:40
SteevenSteeven
3751315
edited Mar 12 at 8:32
answered Mar 11 at 10:40
SteevenSteeven
3751315
answered Mar 11 at 10:40
SteevenSteeven
3751315
answered Mar 11 at 10:40
SteevenSteeven
3751315
3751315
add a comment |
add a comment |
$begingroup$
The angle between $f$ and the $x$-axis is equal to $theta$ because they are both complementary to the angle between $N$ and the $x$-axis. The angle in the fourth quadrant is equal to $theta$ because alternate interior angles are equal.
answered Mar 12 at 8:43
John DoumaJohn Douma
5,59711419
$endgroup$
add a comment |
$begingroup$
The angle between $f$ and the $x$-axis is equal to $theta$ because they are both complementary to the angle between $N$ and the $x$-axis. The angle in the fourth quadrant is equal to $theta$ because alternate interior angles are equal.
answered Mar 12 at 8:43
John DoumaJohn Douma
5,59711419
$endgroup$
add a comment |
$begingroup$
The angle between $f$ and the $x$-axis is equal to $theta$ because they are both complementary to the angle between $N$ and the $x$-axis. The angle in the fourth quadrant is equal to $theta$ because alternate interior angles are equal.
answered Mar 12 at 8:43
John DoumaJohn Douma
5,59711419
$endgroup$
The angle between $f$ and the $x$-axis is equal to $theta$ because they are both complementary to the angle between $N$ and the $x$-axis. The angle in the fourth quadrant is equal to $theta$ because alternate interior angles are equal.
answered Mar 12 at 8:43
John DoumaJohn Douma
5,59711419
answered Mar 12 at 8:43
John DoumaJohn Douma
5,59711419
answered Mar 12 at 8:43
John DoumaJohn Douma
5,59711419
answered Mar 12 at 8:43
John DoumaJohn Douma
5,59711419
5,59711419
add a comment |
add a comment |
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1
$begingroup$
This is a plane geometry problem.
$endgroup$
– user45664
Mar 11 at 20:17