Figuring Out Increase in Angle of Inclination

AI Thread Summary
The acceleration of an object on an inclined plane is determined by the angle of inclination, with the formula a = g sin θ indicating that as the angle increases, so does the acceleration. The angle of inclination, representing the steepness of the slope, ranges from 0 degrees (flat) to 90 degrees (vertical). As a skier descends a hill, the angle of inclination increases, leading to greater acceleration, particularly at steeper angles. Understanding the relationship between angle and acceleration can be aided by visualizing the unit circle, where larger angles yield higher sine values, thus increasing acceleration. The discussion clarifies that the angle of inclination increases when moving down a slope, not up.
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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