This problem describes one experimental method for determining the moment of inertia of an irregularly shaped object such as the payload for a satellite. The figure below shows a counterweight of mass m suspended by a cord wound around a spool of radius r, forming part of a turntable supporting the object. The turntable can rotate without friction. When the counterweight is released from rest, it descends through a distance h, acquiring a speed v. Show that the moment of inertia I of the rotating apparatus (including the turntable) is I = mr'(2gh/v²-1)

This problem describes one experimental method for determining the moment of inertia of an irregularly shaped object such as the payload for a satellite. The figure below shows a counterweight of mass m suspended by a cord wound around a spool of radius r, forming part of a turntable supporting the object. The turntable can rotate without friction. When the counterweight is released from rest, it descends through a distance h, acquiring a speed v. Show that the moment of inertia I of the rotating apparatus (including the turntable) is I = mr'(2gh/v²-1)

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter11: Angular Momentum

Section: Chapter Questions

Problem 72P: An ice skater is preparing for a jump with turns and has his arms extended. His moment of inertia is...

See similar textbooks

Similar questions

A gymnast does cartwheels along the floor and then launches herself into the air and executes several flips in a tuck while she is airborne. If her moment of inertia when executing the cartwheels is 13.5kgm2 and her spin rate is 0.5 rev/s, how many revolutions does she do in the air if her moment of inertia in the tuck is 3.4kgm2 and she has 2.0 s to do the flips in the air?
An ice skater is preparing for a jump with turns and has his arms extended. His moment of inertia is 1.8kgm2 while his arms are extended, and he is spinning at 0.5 rev/s. If he launches himself into the air at 9.0 m/s at an angle of 45 with respect to the ice, how many revolutions can he execute while airborne if his moment of inertia in the air is 0.5kgm2 ?
A massless tether with a masses tied to both ends rotates about a fixed axis through the center. Can the total acceleration of the tether mass combination be zero If the angular velocity Is constant?
If a rigid body has a constant angular acceleration, what is the functional form of the angular velocity In terms of the time variable?
A large turntable rotates about a fixed vertical axis, making one revolution in 5.50s. A child of mass 32.0 kg, initially standing at the center of the turntable, runsout along a radius. When the child is 2.10 m from the center, the turntable makesone revolution in 6.70 s. What is the moment of inertia of the turntable? Note thatyou can treat the child as a point particle.
This problem describes one experimental method for determining the moment of inertia of an irregularly shaped object such as the payload for a satellite. As shown a counterweight of mass m suspended by a cord wound around a spool of radius r, forming part of a turntable supporting the object. The turntable can rotate without friction. When the counterweight is released from rest, it descends through a distance h, acquiring a speed υ. Show that the moment of inertia I of the rotating apparatus (including the turntable) is mr2(2gh/υ2 - 1).
The block on a smooth inclined plano is moving down with a constant acceleration of 6 mis². The block on the inclined plane is 37 kg and the hanging mass is 15 kg. The radius of the pulley is 0.34 m. The angle theta is 24 degreas. Determine the moment of inoria of the pulley. ROUND OFF FINAL ASWER UP TO 2 DECIMAL PLACES. INPUT THE NUMBER ONLY.
In a popular amusement parkride, a rotating cylinder ofradius 3.00 m is set in rotationat an angular speed of5.00 rad/s, as in Figure P7.73.The floor then drops away,leaving the riders suspendedagainst the wall in a verticalposition. What minimum coefficientof friction between arider’s clothing and the wall isneeded to keep the rider fromslipping? Hint: Recall that themagnitude of the maximum force of static friction is equal tomsn, where n is the normal force—in this case, the force causingthe centripetal acceleration.
A mass, m₁ = 8.00 kg, is on a 30.0° incline and it is attached to another mass, m₂ = 10.0 kg, on a 60.0° incline. They are attached with a massless rope over a pulley with a moment of inertia, I, and a radius of R = 0.250 m. There is no friction between the table and the blocks. Ignore air friction, too. We are given that my accelerates up the incline at a = 1.00 m/s². (a) Draw a free-body diagram for both masses and the extended free-body diagram for the pulley. (b) Determine T₁ and T₂. (c) Find the net torque acting on the pulley and (d) its moment of inertia.
The block on a smooth inclined plane is moving down with a constant acceleration of 4 m/s. m, m, The block on the inclined plane is 32 kg and the hanging mass is 19 kg. The radius of the pulley is0 40 m The angle theta is 33 degress. Determine the moment of inertia of the pulley. ROUND OFF FINAL ASWER UP TO 2 DECIMAL PLACES. INPUT THE NUMBER ONLY.
The top in Figure P8.55 has amoment of inertia of 4.00 x10-4 kg . m2 and is initially atrest. It is free to rotate abouta stationary axis AA'. A stringwrapped around a peg alongthe axis of the top is pulled insuch a manner as to maintaina constant tension of 5.57 Nin the string. If the string doesnot slip while wound aroundthe peg, what is the angular speed of the top after 80.0 cm ofstring has been pulled off the peg? Hint: Consider the workthat is done.
A block of mass m = 2.90 kg is hanging from a massless cord that is wrapped around a pulley (mass = 5.00 kg) asshown in the figure. The cord does not slip relative to the pulley as the block falls. Find the magnitude of the tension inthe cord. (moment of inertia of the pulley = ½Mr?)