Rods each of length and mass M, are connected to a hoop of mass M and radius L_t

Question

Rods each of length and mass M, are connected to a hoop of mass M and radius L_to from a S pocket wheel express all answers in terms of the given variables and fundamental constants. give the tot the moment of inertia for the entire spooked -wheel assembly log an axis of notation through the center of the assembly and perpendicular to the plane of the wheel. center of the wheel is now mounted to a frictionless fixed axle and suspended from art support. Sex oral turns of light cord are wrapped around the wheel, and a mass M is attached the end of the cord and allow end to hang. I he mass is released tromp rest. c) Write ail expression for the angular acceleration of the wheel as the mass descends. Write an expression for the instantaneous velocity of the mass after the wheel has turned one revolution.

Explanation / Answer

there are 4 rods and a circular ring.

net moment of inertia=4*moment of inertia of each rod+moment of inertia of a circular ring

=4*(M*L^2/12)+M*(L/2)^2

=7*M*L^2/12

part b:

let tension in the string be T and acceleration of the mass is a.

then writing force balance equation for mass M:

M*g-T=M*a

==>T=M*(g-a)..(1)

for the wheel:

torque=moment of inertia*angular acceleration

==>T*L/2=(7*M*L^2/12)*(a/(L/2))

==>T=(7/3)*M*a...(2)

using equation 2 in equation 1:

(7/3)*M*a=M*(g-a)

==>(7/3)*a+a=g

==>a=0.3*g

hence T=(7/3)*M*0.3*g=0.7*M*g...(ans)

part c:

angular acceleration=linear accleeration/radius=a/(L/2)

=2*a/L=2*0.3*g/L=0.6*g/L

part d:

angle covered in one revolution=2*pi radian

as initial angular speed=0,

using the formula:
final angular speed^2-initial angular speed^2=2*angular acceleration*angle covered

==>final angular speed^2=2*(0.6*g/L)*2*pi=2.4*pi*g/L

hence angular speed after one revolution=sqrt(2.4*pi*g/L)

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.