Athin uniform cylindrical turntable of radius 3.3 m and mass 28 kg rotates in a horizontal plane with an initial angular speed of 8.5 rad/s. the turntable bearing is frictionless. a clump of clay of mass 10 kg is dropped onto the turntable and sticks at a point 1.8 m from the point of rotation. find the angular speed of the clay and turntable. calculate the loss of energy to thermal energy.

The angular speed is 7.01 rad/s

The loss of energy to thermal energy is 965.6 J

Explanation:

Conservation of angular momentum says that 'the angular momentum must be the same before and after the clump of clay is attached to the turntable'.

The angular momentum is defined as: L = I*ω

with I = the moment of inertia

with w= the angular speed

The angular momentum before must be equal to the angular momentum after.

Angular momentum before: Lb = It*ω0

Angular momentum after: La = (It + Ic)*ω1

So Lb = La⇔ It*ω0  = (It + Ic)*ω1

with ω1 = the angular speed after (ω1 = ω0*[It/(It + Ic)])

ω₁ = I₀ω₀ / I₁

I₀ = The moment of inertia of the turntable

= The moment of inertia of a cylinder with mass m and radius r around its z axis = ½mr²., and can be calculated as followed:

I₀ = ½(28)(3.3)² = 152.46 kgm²

I₁ = I₀ + I(clay) = 152.46kgm² + m(clay)*r(clay)² = 152.46 kgm² + (10)(1.80)² = 184.86 kgm²

To calculate ω₁ we use the following formula:

ω₁ = I₀ω₀ / I₁ = 152.46*8.5/ 184.86 = 7.01 rad/s

Calculate the loss of energy to thermal energy

Energy is not conserved. Some amount of energy is lost when the clay deforms and sticks to the turntable! This change in energy is given by:

Et= E₁ - E₀  = (0.5)(184.86)(11.078)² - (0.5)(61.8)(4π)² = -577.94 J

with  E₁= ½I₁ω₁² = ½ * 184.86 * 7.01² = 4542.02

with E₀ = ½I₀ω₀² =  ½ * 152.46 *8.5² = 5507.62

Et= E₁ - E₀ = 4542.02 - 5507.62 = - 965.6 J

This value is negative, this means there is 965.6 J energy lost to thermal energy

quantum mechanics or quantum physics is physics of very small objects (particles) and physical entities.

quantum physics has some parallels to our macro world and some pretty unique ideas which theoretically and mathematically proven to be true even though we will never be able to access them because of our size.

there are many types of particles: subatomic, elementary etc.

subatomic means they are smaller than atom, elementary means they are at the very basis of everything.

subatomic particles are for eg. protons, neutrons but not electrons.

elementary particles are categorised into 3 groups by what they do.

these 3 groups are quarks, leptons and bosons.

light for example is a particle more precisely a photon a part of leptons.

proton (subatomic particle) is made out of 2 up quarks and 1 down quark each of these has a fractional charge like . (i crazy)

most famous scientist who contributed to this physics are:

the topic itself us understand a lot and will probably be vastly used in the future (quantum computers, understanding the big bang,

we also must not forget quantum effects like:

and there is more. but probably too much for this answer to be consistent due to my average understanding of this topic.

hope this you understand quantum mechanics a little more. i'm not an expert in the topic (so don't be like wth if you are an expert) but i'm very interested in it.

anyways quantum physics is a very hard topic (harder than physics (perhaps)) therefore searching for every information there is about it and learning it is unfortunately impossible (you can only specialise into 1 - 3 things or more (perhaps

have fun and i wish you luck!

r3t40

true is the correct answer

hope i