10.4 Rotational Kinetic Energy: Work and Energy Revisited

10.4 Rotational Kinetic Energy: Work and Energy Revisited

  • In terms of revolutions per 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- In the first case, the father would run at 50 km/h.
    • Confirmation of these numbers is an exercise for the reader.
  • Moment of inertia is the analog of mass.
    • The quantities of force and mass are dependent on one factor.
    • Mass is related to the number of atoms in an object.
  • Torque is determined by three factors: force magnitude, force direction, and point of application.
    • The analogies are precise, but the quantities depend on more factors.
  • We will learn about work and energy in this module.
    • As layers of steel are cut from the pole, sparks are flying and noise is created.
    • After the motor is turned off, the stone continues to turn, but it is eventually brought to a stop.
    • The motor had to work to get the stone spinning.
  • The motor is spinning the grindstone.
    • The energy is converted to other things.
  • There is work to be done to rotate objects.
    • When considering work done in rotational motion, we can build on the knowledge that work was defined in for translational motion.
  • The equation is used for rotational work.
    • It is similar to the definition of translation work, which is force multiplied by distance.
    • Torque is similar to force and angle is similar to distance.
  • To get an expression for rotational kinetic energy, we need to perform some algebraic manipulations.
  • The net force on this disk is constant as the disk rotates.
    • The net work is done.
    • The work goes into energy.
  • The work and energy in rotation are the same as the work and energy in translation.
  • We solved one of the equations.
  • Net work changes the energy of a system.
  • The expression for rotational kinetic energy is the same as the expression for translational kinetic energy.
    • The effects of rotational energy are important.
  • This bus is an example of a vehicle that stores energy in a large flywheel.
  • When the bus goes down a hill, the transmission converts its potential energy into something else.
    • When the bus stops, it can convert the energy into.
    • The energy from the flywheel can be used to accelerate, go up another hill, or keep the bus from slowing down.
  • The change in rotational energy is equal to the work done by the Torque she exerts.
    • The force is kept the same at the point of application as it was at the beginning.
  • The equation can be used to find the work.
    • We have enough information to calculate the Torque and rotation angle.
    • In the second part, we can find the final velocity using one of the relationships.
    • In the last part, we can calculate the rotational energy from its expression.
  • The angle is given.
  • A person is grasping the outer edge of a large grindstone.
  • It takes more than one step to find the information.
  • We start from rest.
  • The expression for energy could have been used to solve part b.
    • In later examples, we will do this.
  • Helicopter pilots are familiar with this energy.
    • They know that a point of no return will be reached if they allow their blades to slow.
    • It is difficult to get the blades to spin fast enough to regain lift.
    • Enough energy can't be supplied in time to avoid a crash because the rotational energy must be supplied to the blades.
    • Because of weight limitations, helicopter engines are too small to supply both the energy needed for lift and to replenish the energy of the blades once they have slowed down.
    • They must not be allowed to drop below this crucial level if they want to take off.
    • One way to avoid a crash is to use the helicopter's potential energy to replenish the blades by losing altitude and aligning them so that they spin up in the descent.
  • If the helicopter's altitude is too low, there is not enough time for the blade to regain lift before reaching the ground.
  • Determine if work or energy is involved in the rotation.
  • The system of interest should be determined.
    • A sketch can help.
  • Determine the types of work and energy involved in the situation.
  • The mechanical energy of closed systems is conserved.
  • If possible, eliminate the terms.
  • The answer should be checked to see if it is reasonable.
  • The blades can be compared to thin rods that rotation one end of an axis to their length.
    • There is a helicopter with a loaded mass of 1000 kilograms.
  • They can be calculated from their definitions.
    • The idea that energy can change form is related to the last part of the problem.
  • The moment of inertia must be calculated before we can find it.
  • There are four blades and the total is four times this moment of inertia.
  • The translational energy was defined in motion.
  • We take the ratio of the two energy types to compare.
  • All of the energy from the rotation will be converted to the force of gravity at the maximum height.
  • The ratio of energy to energy is not very high.
    • You probably wouldn't suspect that most of the helicopter's energy is in its spinning blades.
    • The helicopter's height of 53.7 m is impressive and shows the amount of energy in the blades.
  • Helicopters store large amounts of energy in their blades.
    • The energy must be put into the blades before the plane takes off.
    • The engines don't have enough power to put a lot of energy into the blades.
    • The second image shows a helicopter.
    • Over 50,000 lives have been saved since 1973.
    • A water rescue operation is shown.
  • The treatment of energy is covered in Uniform Circular Motion and Gravitation.
  • A tomato soup factory has a quality control that involves rolling filled cans down a ramp.
    • The soup is too thin if they roll fast.
  • Energy is the easiest way to answer these questions.
    • Each can start from the rest.
    • Each can starts with the same potential energy, which is converted to 888-492-0 888-492-0 if each rolls without slipping.
  • When a can rolls down a ramp, it puts part of its energy into rotation.
    • The thick soup sticks to the can, while the thin soup does not.
  • It wins because it converts its PE into something else.
    • The second and third cans roll down the incline.
    • The thin soup in the second can comes in second because part of its initial PE goes into rotating the can.
    • The soup in the third can is thick.
    • The soup rotates along with the can, taking more of the initial PE for rotational KE, leaving less for translation.
  • gravity is the only force doing work.
    • The change in energy is the total work done.
    • The potential energy is changing as the cans move.
  • The more energy goes into translation, the less it goes into the initial.
    • All the energy goes into translation if the can slides down.
  • Different types of food can be found in cans.
    • Predict which can win the race and explain why.
    • If your prediction is correct, check it out.
    • You could fill the empty containers with different materials such as wet or dry sand for the experiment.
  • Determine the final speed of a cylinder that rolls down a high incline.
    • The cylinder has a mass of 0.750 kilogram and a radius of 4.00 cm.
  • We can solve for the final velocity with the use of energy, but we must first express rotational quantities in terms of translational quantities to end up with as the only unknown.
  • We need to get an expression for from Figure 10.
    • We need to substitute the relationship into the expression because the cylinder is rolling without slipping.