Question

) A 1.53-kg bucket hangs on a rope wrapped around a pulley of mass 7.07 kg and radius 66 cm.   This pulley is frictionless in its axle, and has the shape of a solid uniform disk. After the bucket has been released, what is the angular acceleration of the pulley?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the bucket = m = 1.53 kg

Mass of the pulley = M = 7.07 kg

Radius of the pulley = R = 66 cm = 0.66 m

Moment of inertia of the pulley = I

I = MR²/2

I = (7.07)(0.66)²/2

I = 1.54 kg.m²

Tension in the rope = T

Angular acceleration of the pulley =

Acceleration of the bucket = a

a = R

For the bucket,

ma = mg - T

T = mg - ma

T = m(g - R)

For the pulley,

I = TR

I = m(g - R)R

(1.54) = (1.53)(0.66)(9.81 - 0.66)

1.54 = 9.906 - 0.666

= 4.489 rad/s²

Angular acceleration of the pulley = 4.489 rad/s²