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Rolling on Inclined Plane

Calculation of duration and velocity of an object rolling down a slope (inclined plane). Friction is neglected. The velocity is the speed of the object at the length l. This calculation only applies if the inclined plane is straight, i.e. the rolling object moves in a straight line. On curved surfaces, different speeds and accelerations are achieved.


Rollen auf schiefer Ebene

Slope Calculation:


The angle of inclination of the inclined plane can be calculated from the length of the slope and the vertical height. The formula is: h = h = l * sin (α), with the conditions l>h and 0°<α<90°.

Length l: m
Height h: m
Angle of slope α: °

Please enter two values, the third value will be calculated. Here you can convert angle units.

Calculation of Velocity v:


There are several ways to calculate the speed. One of them calculates it from the height that has already been covered downwards. The formula for this is: v = √ g * h / ( 1/2 + c ) , the local gravity factor g is calculated as 9.81 m/s²

Velocity v: m/s
Height h: m
Shape factor c:

Please enter velocity or height, the other value will be calculated. The shape factor for a massive ball is 0.4, for a massive cylinder it is 0.5. Here you can convert velocity units (e.g. in mph).

Time Calculation:


The time is the duration needed to roll down the plane with length l. l is also the distance that is rolled. The speed is calculated using the following formula: t = 2 * l / v
This formula differs from the usual formula for the speed v=s/t (with s instead of l) by a factor of 2. The reason for this is that the specified speed is the final speed. However, if you start with a speed of 0, then the average speed is half the final speed, so the time required is twice as long.

Time t: s
Velocity v: m/s
Length: m

Please enter two values, the third value will be calculated.

Example: at a length of 10 and a height of 5 meters, the angle of slope is 30°, the velocity of a ball is 7.3824 m/s and the time to get there is 2.7091 seconds.




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