Figuring Out Increase in Angle of Inclination

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SUMMARY

The discussion focuses on understanding the relationship between the angle of inclination and the acceleration of an object sliding down an inclined plane, specifically in the context of skiing. The acceleration is defined by the formula a = g sin θ, where g represents gravitational acceleration. As the angle of inclination increases, so does the acceleration of the skier. The conversation clarifies that the angle of inclination is measured from the horizontal, with 0 degrees being flat and 90 degrees being vertical, affecting the skier's speed and acceleration significantly.

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  • Understanding of basic physics concepts, particularly forces and motion.
  • Familiarity with trigonometric functions, especially sine.
  • Knowledge of gravitational acceleration (g) and its implications in motion.
  • Basic comprehension of inclined planes and their effects on objects in motion.
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  • Study the principles of inclined planes in classical mechanics.
  • Learn about the unit circle and its application in trigonometry.
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  • Investigate real-world applications of angle of inclination in sports, such as skiing and cycling.
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Temper888
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Hey Guys,

I was doing physics questions. It was written that in the absence of friction, the acceleration of any object sliding down an inclined plane is given by:a=gsinθ. As the skier skis down the curved hill, the angle of inclination is increasing, so the acceleration of the skier is increasing. What I cannot figure out is how to know when the angle of inclination is increasing. For instance, I thought angle of inclination should increase while going up an incline. Could you please say me if there is a method of figuring out how a certain way(up or down) the incline leads to an increase or decrease in angle of inclination?

Thanks
 
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The angle of inclination means the 'steepness' of the slope and is usually measured from the horizontal.
So a slope that is not very steep may be 10degrees and a steep slope may be 60 degrees.
Flat (no slope) is 0 degrees, vertical is 90 degrees
 
If the skier is coming down the hill at a 10° angle he would be going slower than if he were to be going down at a 60° angle due to the work of his weight.
 
In other words you said that a=gsinθ. Try to think of the unit circle; the bigger the angle, the closer the sinus gets close to 1 but only between pi and pi/2.
 
If the angle of the slope is 0 degrees he will not be accelerating due to his weight (Sine0 =0)
If the angle of the slope is 90 degrees (vertical) he will be falling freely under gravity and his acceleration will be = g (Sine90 =1)
If the slope is 30 degrees his acceleration will be g/2 (Sine30 = 0.5)
And so on...
 
technician said:
If the angle of the slope is 0 degrees he will not be accelerating due to his weight (Sine0 =0)
If the angle of the slope is 90 degrees (vertical) he will be falling freely under gravity and his acceleration will be = g (Sine90 =1)
If the slope is 30 degrees his acceleration will be g/2 (Sine30 = 0.5)
And so on...

Yea kind of what I was trying to tell him but you explained it better.
 

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