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The correct answer is Equal to each other. In physics, friction is the resistive force that opposes motion between two surfaces in contact. Two important angles related to friction are the angle of friction and the angle of repose.
The angle of friction (θf) is defined as the angle made by the resultant of normal and frictional forces with the normal when a body is on the verge of sliding on a horizontal surface. It represents the maximum inclination at which a body can rest before sliding begins.
The angle of repose (θr) is the maximum angle of inclination at which a body can remain at rest on an inclined plane without sliding. It is determined by gradually increasing the slope until the body just starts to slide.
Mathematically, both angles are related to the coefficient of friction (μ) as:
μ=tanθf=tanθr\mu = \tan \theta_f = \tan \theta_rμ=tanθf=tanθr
This equation shows that the angle of friction and the angle of repose are equal to each other, because both describe the same physical condition—when motion is about to start due to friction.
Understanding these angles is essential in engineering, mechanics, and material handling, as they help in designing slopes, ramps, and surfaces to prevent slipping. For example, calculating the angle of repose is important in storing granular materials like sand, grains, or coal to ensure stability of heaps and prevent accidents.
Angle of friction (θf) = maximum angle on a horizontal surface before sliding.
Angle of repose (θr) = maximum slope on an inclined plane before sliding.
θf = θr mathematically.
Related to coefficient of friction: μ = tan θ.
Important for mechanical design, slope stability, and material storage.
👉 Final Answer: The angle of friction and the angle of repose are Equal to each other.
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