A pulley such as that shown in Figure P82S has rotational in

A pulley such as that shown in Figure P8.2S has rotational inertia 10kg m^2. Three ropes wind around different parts of the pulley and exert forces T_1 on w = 80 N, T, _2on w = 100 N, and T_JonW = 50 N. Determine (a) the rotational acceleration of the pulley and (b) its rotational velocity after 4.0 s. It starts at rest.

Solution

Net Torque on the pulley

T_Net =T_{Counterclockwise} -T_clockwise = 3aT₁-aT₂-2aT₃

T_Net=240a-100a-100a =40a

a)

Angular acceleration

alpha =T/I =40a/10 =4a rad/s²

b)

angular velocity

W=alpha/T =4a*4

W=16a rad/s