Earth has a mass of 6.0 × 10
24 kg, a radius of 6.4 × 10
6 m, and an angular velocity of 1.2 × 10
–5 rev/s. How would the planet's angular velocity change if a layer of Earth with mass 1.0 × 10
23 kg broke off of the Earth, decreasing Earth's radius by 0.2 × 10
6 m? Assume no friction.
Consider system A, consisting of two disks of radius
R , with both rotating clockwise. Now consider system B, consisting of one disk of radius
R rotating counterclockwise and another disk of radius 2
R rotating clockwise. All of the disks have the same mass, and all have the same magnitude of angular velocity.
Assume that a baseball bat being swung at 3π rad/s by a batting machine is equivalent to a 1.1 m thin rod with a mass of 1.0 kg. How fast would a 0.15 kg baseball that squarely hits the very tip of the bat have to be going for the net angular momentum of the bat-ball system to be zero?
Every rotational phenomenon has a direct translational analog , likewise angular momentum
can be defined as
This equation is an analog to the definition of linear momentum as
. The relationship between torque and angular momentum is
Angular momentum, like energy and linear momentum, is conserved. This universally applicable law is another sign of underlying unity in physical laws. Angular momentum is conserved when net external torque is zero, just as linear momentum is conserved when the net external force is zero.
Conceptual questions
When you start the engine of your car with the transmission in neutral, you notice that the car rocks in the opposite sense of the engine's rotation. Explain in terms of conservation of angular momentum. Is the angular momentum of the car conserved for long (for more than a few seconds)?
Suppose a child walks from the outer edge of a rotating merry-go round to the inside. Does the angular velocity of the merry-go-round increase, decrease, or remain the same? Explain your answer.
A child may jump off a merry-go-round in a variety of directions.
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? (b) He jumps backward to land motionless? (c) He jumps straight up and hangs onto an overhead tree branch? (d) He jumps off forward, tangential to the edge? Explain your answers. (Refer to
[link] ).
Helicopters have a small propeller on their tail to keep them from rotating in the opposite direction of their main lifting blades. Explain in terms of Newton's third law why the helicopter body rotates in the opposite direction to the 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?
I am a university student of Myanmar.I am first year,first semester.I want to learn about physics.
Maung
two charges qA and qB are separated by a distance x. if we double the distance between the charges and triple the magnitude of the charge A, what happens to the magnitude of the force that charge A exerts on charge B.
what happens to the magnitude of the force that charge B exerts on charge A
a reflected ray on a mirror makes an angle of 20degree with the incident ray when the mirror is rotated 15degree what angle will the incident ray now make with the reflected ray
Roofs are sometimes pushed off vertically during a tropical cyclone, and buildings sometimes explode outward when hit by a tornado. Use Bernoulli’s principle to explain these phenomena.
Insulators (nonmetals) have a higher BE than metals, and it is more difficult for photons to eject electrons from insulators. Discuss how this relates to the free charges in metals that make them good conductors.
