Question

To be able to solve problems involving force, moment, velocity, and time by applying the principle of impulse and momentum to rigid bodies. The principle of impulse and momentum states that the sum of all impulses created by the external forces and moments that act on a rigid body during a time interval is equal to the change in the linear and angular momenta of the body during that time interval. In other words, impulse is the change in momentum. The greater the impulse exerted on a body, the greater the body’s change in momentum. For example, baseball batters swing hard to maximize the impact force and follow through to maximize the impact time. This principle holds true for both linear and angular impulse and momentum. For a rigid-body’s planar motion, the equations for the linear impulse and momentum in the x–y plane are given by m(vGx)1+∑∫t2t1Fxdt=m(vGx)2 m(vGy)1+∑∫t2t1Fydt=m(vGy)2 Similarly, the equation for the principle of angular impulse and momentum about the z axis, which passes through the rigid-body’s mass center G, is given by IGω1+∑∫t2t1MGdt=IGω2

Answer 1

Answer:

see explaination

Explanation:

Please kindly check attachment for the step by step solution of the given problem.

The attached files has the solved problem.

Answer 2

Answer: 3.33T rad/s

Explanation:

here is a step by step explanation for the problem.

we have that the Moment of inertia of the pulley Ia = 0.225 Kg-m³

                                           Radius of the pulley r = 0.15m

                                           Mass of the pulley m = 20 Kg

we know that the torque acting on the pulley (Tr) = Iα

where α = Tr/ I

here, T is the tension of the cord,

also α is the angular acceleration ,

also, I is the moment of inertia and r is  the radius.

from 2nd rotational kinematics law;

ω₂ = ω₁ + αt .................. (1)

given that ω₂ and ω₁ is the final and inertia angular velocity, t is the time.

note: initial velocity (ω₁) is zero since system is at rest.

now from the expression in (1)

ω₂ = ω₁ + αt

= (0) + (Tr/I)t

ω₂ = (T(0.15) / 0.225 )*(5) = 3.33T rad/s

from this we can say that the angular velocity of the pulley is 3.33T rad/s at t = 5sec

cheers i hope this helps!!!!