Angular momentum has which of the following units

In figure A, there is a merry go round. A child is jumping radially outward. In figure B, a child is jumping backward to the direction of motion of merry go round. In figure C, a child is jumping from it to hang from the branch of the tree. In figure D, a child is jumping from the merry go round tangentially to its circumference.

Suppose a child gets off a rotating merry-go-round. Does the angular velocity of the merry-go-round increase, decrease, or remain the same if: a He jumps off radially? Explain your answers. Refer to Figure 6. Helicopters have a small propeller on their tail to keep them from rotating in the opposite direction of their main lifting blades. Whenever a helicopter has two sets of lifting blades, they rotate in opposite directions and there will be no tail propeller.

Explain why it is best to have the blades rotate in opposite directions. Describe how work is done by a skater pulling in her arms during a spin. In particular, identify the force she exerts on each arm to pull it in and the distance each moves, noting that a component of the force is in the direction moved.

Why is angular momentum not increased by this action? When there is a global heating trend on Earth, the atmosphere expands and the length of the day increases very slightly. Explain why the length of a day increases. Nearly all conventional piston engines have flywheels on them to smooth out engine vibrations caused by the thrust of individual piston firings.

Why does the flywheel have this effect? Jet turbines spin rapidly. Explain how flying apart conserves angular momentum without transferring it to the wing. An astronaut tightens a bolt on a satellite in orbit. He rotates in a direction opposite to that of the bolt, and the satellite rotates in the same direction as the bolt. Explain why. If a handhold is available on the satellite, can this counter-rotation be prevented? Competitive divers pull their limbs in and curl up their bodies when they do flips.

Just before entering the water, they fully extend their limbs to enter straight down. Explain the effect of both actions on their angular velocities. Also explain the effect on their angular momenta. Figure 7. The diver spins rapidly when curled up and slows when she extends her limbs before entering the water.

Draw a free body diagram to show how a diver gains angular momentum when leaving the diving board. In terms of angular momentum, what is the advantage of giving a football or a rifle bullet a spin when throwing or releasing it? Figure 8. The image shows a view down the barrel of a cannon, emphasizing its rifling. Rifling in the barrel of a canon causes the projectile to spin just as is the case for rifles hence the name for the grooves in the barrel.

Remember that the Moon keeps one side toward Earth at all times. Suppose you start an antique car by exerting a force of N on its crank for 0. What angular momentum is given to the engine if the handle of the crank is 0.

A playground merry-go-round has a mass of kg and a radius of 1. What is its angular velocity after a The child is initially at rest. Three children are riding on the edge of a merry-go-round that is kg, has a 1.

The children have masses of If the child who has a mass of Find the value of his moment of inertia if his angular velocity decreases to 1. What average torque was exerted if this takes Construct a problem in which you calculate the total angular momentum of the system including the spins of the Earth and the Moon on their axes and the orbital angular momentum of the Earth-Moon system in its nearly monthly rotation.

The angular momentum of the Earth in its orbit around the Sun 3. Skip to main content. Rotational Motion and Angular Momentum. Search for:. Angular Momentum and Its Conservation Learning Objectives By the end of this section, you will be able to: Understand the analogy between angular momentum and linear momentum.

Observe the relationship between torque and angular momentum. Apply the law of conservation of angular momentum. At some instant a viscous fluid of mass m is dropped at the centre and is allowed to spread out and finally fall out. The angular velocity during the period.

Which of the following is the product of moment of inertia and angular velocity? A thin ring of mass 5 kg and diameter 20 cm is rotating about its axis at rpm. The circumference of a planet is 36, km. If the planet makes no other movement and takes 20 hours for one complete rotation, what is the speed of a point on its equator? More Rotational Motion Questions Q1. The moment of inertia of a rigid body depends on-. The square root of the ratio of moment of inertia of the cross section to its cross-sectional area is called.

For a conservative holonomic dynamical system, the Lagrangian L, kinetic energy T and potential energy V are connected by. The torque experienced by a magnetic dipole, having dipole moment M, when placed in a uniform magnetic field of intensity B is:. The correct relation is- L: Angular momentum, r is radius, p: Linear momentum.

If the radius of earth is km. Suggested Test Series. First, however, we investigate the angular momentum of a single particle. This allows us to develop angular momentum for a system of particles and for a rigid body that is cylindrically symmetric.

Even if the particle is not rotating about the origin, we can still define an angular momentum in terms of the position vector and the linear momentum. Figure The magnitude of the angular momentum is found from the definition of the cross-product,. In this respect, the magnitude of the angular momentum depends on the choice of origin. If we take the time derivative of the angular momentum, we arrive at an expression for the torque on the particle:.

The following problem-solving strategy can serve as a guideline for calculating the angular momentum of a particle. We resolve the acceleration into x — and y -components and use the kinematic equations to express the velocity as a function of acceleration and time. We insert these expressions into the linear momentum and then calculate the angular momentum using the cross-product.

Since the position and momentum vectors are in the xy -plane, we expect the angular momentum vector to be along the z -axis. To find the torque, we take the time derivative of the angular momentum. This is the instant that the observer sees the meteor. The units of torque are given as newton-meters, not to be confused with joules. Since the meteor is accelerating downward toward Earth, its radius and velocity vector are changing.

This example is important in that it illustrates that the angular momentum depends on the choice of origin about which it is calculated. The methods used in this example are also important in developing angular momentum for a system of particles and for a rigid body. A proton spiraling around a magnetic field executes circular motion in the plane of the paper, as shown below.

The circular path has a radius of 0. What is the angular momentum of the proton about the origin? Show Answer. The angular momentum of a system of particles is important in many scientific disciplines, one being astronomy. Consider a spiral galaxy, a rotating island of stars like our own Milky Way. The individual stars can be treated as point particles, each of which has its own angular momentum.

The vector sum of the individual angular momenta give the total angular momentum of the galaxy. In this section, we develop the tools with which we can calculate the total angular momentum of a system of particles. In the preceding section, we introduced the angular momentum of a single particle about a designated origin.

That is,. Figure states that the rate of change of the total angular momentum of a system is equal to the net external torque acting on the system when both quantities are measured with respect to a given origin. Figure can be applied to any system that has net angular momentum, including rigid bodies, as discussed in the next section. Referring to Figure a , determine the total angular momentum due to the three particles about the origin.

Write down the position and momentum vectors for the three particles. Calculate the individual angular momenta and add them as vectors to find the total angular momentum. Then do the same for the torques. This example illustrates the superposition principle for angular momentum and torque of a system of particles.

We have investigated the angular momentum of a single particle, which we generalized to a system of particles. Now we can use the principles discussed in the previous section to develop the concept of the angular momentum of a rigid body. Celestial objects such as planets have angular momentum due to their spin and orbits around stars. In engineering, anything that rotates about an axis carries angular momentum, such as flywheels, propellers, and rotating parts in engines.

Knowledge of the angular momenta of these objects is crucial to the design of the system in which they are a part. All mass segments that make up the rigid body undergo circular motion about the z -axis with the same angular velocity.

The rigid body is symmetrical about the z-axis.