A pulley is a part of a convenient arrangement that makes it possible to transfer force with change of direction. Unless otherwise stated, a pulley is considered to have negligible mass and friction. This is a relative approximation with respect to mass and friction involved with other elements. Pulleys are used in different combination with other elements – almost always with strings and blocks.

 

The important characterizing aspects of pulley are as follows;

# Static or fixed pulley

 

#  Moving pulley

 

#  Combination or Multiple pulley system

 

Equations for rotational motion:

(a) ω = ω₀ + αt;

(b) θ = ω₀t +1/2αt²;

(c) ω²- ω₀²=2αθ

 

Centre of mass: For two particle system:

 (a)  x_cm =m₁x₁+m₂x₂/m₁+m₂

 (b)  v_cm=m₁v₁+m₂v₂/m₁+m₂

 (c) a_cm=m₁a₁+m₂a₂/m₁+m₂

Also v_cm=dx_cm/dt and a_cm=dv_cm/dt=d²x_cm/dt

FRICTION

Force of friction:



(a) ƒ_s ≤ μ_sN (self adjusting); (ƒ_s)max = μ_sN



(b) μ_k = μ_kN (μk = coefficient of kinetic friction)



(c) μ_k < μ_s



(i) Acceleration on a horizontal plane: a = (F - μ_kN)/M



(ii) Acceleration of a body sliding on an inclined plane: a = g sin θ (1–- μ_k cot t²)



(iii) Force required to balance an object against wall: F = (Mg/μ_s)



(iv) Angle of friction: tan θ = μ_s (μ_s = coefficient of static friction)