Work, Energy, and Power14–56.A gear with a mass moment of inertia of 0.45 kg⋅m2 has a kinetic energy of rotation of 21 joules. What is its speed of rotation in rpm?14–63.Wheel A in Figure...

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Answered Same DayFeb 23, 2023

Answer To: Work, Energy, and Power14–56.A gear with a mass moment of inertia of 0.45 kg⋅m2 has a kinetic...

Baljit answered on Feb 23 2023
52 Votes
Work, Energy, and Power
14–56.
A gear with a mass moment of inertia of 0.45 kg⋅m2 has a kinetic energy of rotation of 21 joules. Wha
t is its speed of rotation in rpm?
Answer:-
Given
Mass of Inertia ,IC= 0.45 kg⋅m2
Kinetic Energy of rotation, KE=21J
Now we know that
Kinetic Energy of Rotation is
So speed of rotation
=
66 rad/s
Now
So speed of rotation is 92.246 rpm.
14–63.
Wheel A in Figure P14–63 weighs 200 lb and has a radius of gyration of 2 ft. If the system is initially at rest, determine the angular velocity of A after B has dropped 8 ft
Answer:-
Given
Let v ft/s is velocity of B after it dropped 8 ft.
So the angular velocity is
Here r is radius of wheel i.e 3 ft.
So
Now radius of Gyration is k=2ft
So it moment of inertia
Now Weight of wheel W=200 lb
So mass of wheel
So
Moment of inertia
Potential Energy loss of B
Kinetic Energy KEB
Now Kinetic Energy gain of A is
Conservation of energy requires that loss of potential energy of B should be converted into kinetic energy gain of B and A.
So
Angular velocity of A is
So the Angular velocity of A is clockwise.
14–64.
Masses A and B in Figure P14–64 are fastened together by a belt over pulley D. (Assume no slipping of the belt.) The mass moment of inertia of pulley D is 15 kg⋅m2. How far does mass B drop before reaching a velocity of...
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