# Inclined planes

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

## Answers and Replies

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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......

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.