A wheel is rotating freely at angular speed 800 rev/min on ashaft whose rotational inertia is negligible. A secod wheel,initially rest and with twice

Question

A wheel is rotating freely at angular speed 800 rev/min on ashaft whose rotational inertia is negligible. A secod wheel,initially rest and with twice

he298c 2021-04-03 Answered

A wheel is rotating freely at angular speed 800 rev/min on ashaft whose rotational inertia is negligible. A secod wheel,initially rest and with twice the rotational inertia of the first,is suddenly coupled to the same shaft.
A) what is the angular speedof the resultant combination of the shaft and the two wheels?
B)What fraction of the orginial rotational kinetic energy is lost?

Ask Expert 1 See Answers

You can still ask an expert for help

Expert Answer

Clelioo

Answered 2021-04-05 Author has 88 answers

(A) Initial MI = I
Angular speed

ω_{i} = 800 r \pm = 800 \times 60 \times 2 π

rad. / s
MI of second wheel = 2I
So final MI after coupling = 3I
Final angular speed =

ω_{f}

Angular momentum is conserved in the process. So,

| ω_{i} = 3 | ω_{f}

ω_{f} = \frac{ω_{i}}{3} = 800 \times 60 \times \times 2 \frac{π}{3}

= 1.005 \times 10^{5}

rad. /s (or) 266.7 rpm
(B) Initial Rotational KE = 0.5

∣ {(ω_{i})}^{2}

Final Rotational K.E. = 0.5(3|)

{(ω_{f})}^{2}

Fraction of the orginial rotational kinetic energy lostis

= \frac{{(R . K . E .)}_{i} - {(R . K . E .)}_{i}}{{(R . K . E .)}_{i}} = 0.667

This is helpful 78

Relevant Questions

asked 2021-01-17

A golfer hits a golf ball at an angle of 25 degrees to the ground. If the golf ball covers a horizontal distance of 301. 5 m, what is the ball's maximum height? (Hint: at the top of its flight, the ball's vertical velocity component will be zero.)

See answers (2)

asked 2021-02-12

A skier of mass 70 kg is pulled up a slope by a motor driven cable. (a) How much work is required to pull him 60m up a 30 degree slope (assumed frictionless) at a constant speed of 2.0 m/s ?(b) What power must a motor have to perform this task?

See answers (2)

asked 2020-12-25

An Alaskan rescue plane drops a package of emergency rations to a stranded party of explorers. the plane is traveling horizontally at $30.0 m / s$ at a height of $200.0 m$ above the ground.