The children create torques, and to calculate the net torque, we sum their torques, being careful about signs. The plank creates no net torque
since its midpoint is at the fulcrum.Now we use the values we calculated for the net torque and the moment of inertia to calculate the angular acceleration.Because various quantities change, such as the angle between the direction of each child’s weight and the seesaw, the angular acceleration
changes as the seesaw rotates. This is why we asked for the initial angular acceleration.Step Reason
6. ȈIJ = IJG + IJB net torque equals sum of torques
7. ȈIJ = mGgrG + (ímBgrB) equation for torque
8. enter values
9. ȈIJ = 76.6 N·m evaluate
Step Reason
10.Į =ȈIJ / I Newton’s second law for rotation
11.Į = (76.6 N·m)/(379 kg·m^2 ) substitute equations 5 and 9 into equation 10
12.Į = 0.202 rad/s^2 (counterclockwise) solve for Į
10.6 - Interactive problem: close the bridge
Once again, you are King Kong, and your task is to close the bridge you see on the
right in order to save an invaluable load of bananas (well, invaluable to you at least).
Here, we ask you to be a more precise gorilla than you may have been in the
introductory exercise.To close the bridge quickly enough to save the fruit without breaking off the bumper
pilings, you need to apply a torque so that the bridge’s angular acceleration is
ʌ/16.0 rad/s^2. The moment of inertia of the rotating part of the bridge is
45,400,000 kg·m^2.
Two trucks are parked on this part of the bridge, and you must include them when
you calculate the total moment of inertia. Each truck has a mass of 4160 kg; the
midpoint of one is 20.0 m and the midpoint of the other is 30.0 m from the pivot (axis
of rotation) of the swinging bridge. The trucks will increase the bridge's moment of
inertia. To solve the problem, consider all the mass of each truck to be concentrated
at its midpoint.
You apply your force 35.0 m from the pivot and your force is perpendicular to the
rotating component of the bridge. Enter the amount of force you wish to apply to the nearest 0.01×10^5 N and press GO to start the simulation.
Press RESET if you need to try again.
If you have difficulty solving this problem, review the sections on calculating the moment of inertia, and the relation between torque, angular
acceleration, and moment of inertia.10.7 - Physics at work: flywheels
Flywheels are rotating objects used to store energy
as rotational kinetic energy. Recently, environmental
and other concerns have caused flywheels to receive
increased attention. Many of these new flywheels
serve as mechanical “batteries,” replacing traditional
electric batteries.
Why the interest? Traditional chemical batteries,
rechargeable or not, have a shorter total life span
than flywheels and can cause environmental
problems when disposed of incorrectly. On the other
hand, flywheels cost more to produce than traditional
batteries, and their ability to function in demanding
situations is unproven.
Flywheels can be powered by “waste” energy. For instance, when a bus slows down, its brakes warm up. The bus’s kinetic energy becomes
thermal energy, which the vehicle cannot re-use efficiently. Some buses now use a flywheel to convert a portion of that linear kinetic energy
into rotational energy, and then later transform that rotational energy back into linear kinetic energy as the bus speeds up.This advanced flywheel is being developed by NASA as a
source of stored energy for use by satellites and spacecraft.(^194) Copyright 2007 Kinetic Books Co. Chapter 10