All questions of Angular Momentum for EmSAT Achieve Exam

While in the pike position the body decreases in radius as each segment moves closer to the axis of rotation, resulting in angular velocity increasing and a decrease of moment of inertia. Thus, during a dive, angular momentum is constant meaning that moment of inertia is inversely proportional to angular velocity.

To find the speed of the electron, we can use the centripetal force formula:

F = mv²/r

Where F is the centripetal force, m is the mass of the electron, v is the speed of the electron, and r is the radius of the orbit.

The centripetal force is provided by the electrostatic force between the electron and the nucleus. This force is given by Coulomb's law:

F = k * (e² / r²)

Where k is the electrostatic constant, e is the charge of the electron, and r is the radius of the orbit.

Since the centripetal force and the electrostatic force are equal, we can set them equal to each other:

mv²/r = k * (e² / r²)

We can solve this equation for v:

v = √((k * e²) / (m * r))

Plugging in the given values:

k = 8.99 x 10^9 Nm²/C² (electrostatic constant)
e = 1.6 x 10^-19 C (charge of the electron)
m = 9 x 10^-31 kg (mass of the electron)
r = 4.5 x 10^-11 m (radius of the orbit)

v = √((8.99 x 10^9 Nm²/C² * (1.6 x 10^-19 C)²) / (9 x 10^-31 kg * 4.5 x 10^-11 m))

v ≈ 2.19 x 10^6 m/s

Therefore, the speed of the electron is approximately 2.19 x 10^6 m/s.

Conservation of angular momentum is the principle on which spacecraft orientation is based. Angular momentum is a fundamental concept in physics that describes the rotational motion of an object. It is defined as the product of an object's moment of inertia and its angular velocity.

Explanation:
When a spacecraft is in motion, it possesses angular momentum due to its rotation. According to the principle of conservation of angular momentum, the total angular momentum of a system remains constant unless acted upon by an external torque. This means that the spacecraft will continue to rotate at a constant rate unless a torque is applied to change its angular momentum.

In the context of spacecraft orientation, the conservation of angular momentum is crucial for maintaining the stability and control of the spacecraft. Here's how it works:

1. Initial angular momentum: When a spacecraft is launched into space, it has an initial angular momentum that is determined by its moment of inertia and angular velocity.

2. Action and reaction: In the absence of external torques, the spacecraft will continue to rotate at a constant rate due to the conservation of angular momentum. Any action taken by the spacecraft to change its orientation will result in an equal and opposite reaction, as required by Newton's third law of motion.

3. Reaction wheels: To control the spacecraft's orientation, reaction wheels are used. These wheels are motor-driven devices that can change their rotational speed. By spinning the reaction wheels in different directions or changing their speeds, the spacecraft can exert torques on itself and alter its angular momentum.

4. Principle application: By carefully controlling the angular momentum of the reaction wheels, the spacecraft can achieve the desired orientation. For example, if the spacecraft needs to rotate along a particular axis, it can spin one or more reaction wheels in the opposite direction to generate a torque that counteracts the existing angular momentum and causes the spacecraft to rotate.

In conclusion, the conservation of angular momentum is the principle that governs spacecraft orientation. By applying torques through reaction wheels, the spacecraft can change its angular momentum and achieve the desired orientation in space.

Momentum is conserved, but internal kinetic energy is not conserved. (a) Two objects of equal mass initially head directly toward one another at the same speed. (b) The objects stick together (a perfectly inelastic collision), and so their final velocity is zero.