1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zhuklara [117]
3 years ago
15

A uniform solid disk rolls without slipping down an incline making an angle θ with the horizontal. What is its acceleration? (En

ter the magnitude. Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.)
Physics
1 answer:
Maru [420]3 years ago
6 0

Answer:

aCM = (2/3)*g*Sin θ

Explanation:

Consider a uniform solid disk having mass M,  radius R and rotational inertia I  about its center of mass, rolling without  slipping down an inclined plane.

In order to get the linear acceleration of the object’s center of mass, aCM ,

down the incline,  we analyze this as follows:

The force of gravity (W = Mg) acting straight down  is resolved into components parallel and  perpendicular to the incline.

Since the object rolls without  slipping there is a force of  friction (Ff) acting on the object,  at it’s point of contact with the  incline, in the direction up  the incline.

Newton’s 2nd Law gives then for acceleration down the incline

∑Fx' = m*aCM   ⇒    m*g*Sin θ - Ff = m*aCM

The force of friction also causes a torque around the center of mass

having lever arm R so we can also write

τ = R*Ff = I*α

Solving for the friction,    Ff = I*α / R

This is used in the expression  derived from the 2nd Law:

m*g*Sin θ - Ff = m*g*Sin θ - (I*α / R) = m*aCM

The objects angular acceleration is related to the linear acceleration  of the edge that contacts the incline by

a = R*α

Since the object rolls without  slipping this has the same  magnitude as aCM so we have  that

α = aCM / R

Using this in

m*g*Sin θ - (I*α / R) = m*g*Sin θ - (I*(aCM / R) / R) = m*aCM

⇒  aCM = (m*g*Sin θ*R²) / (I + m*R²)

if I = (1/2)*m*R²   (for a uniform solid disk)

we get

aCM = (2/3)*g*Sin θ

You might be interested in
The mass of a coin is measured to be 12.5±0.1 g. The diameter is 2.8±0.1 cm and the thickness 2.1 ±0.1 mm. Calculate the average
Evgesh-ka [11]

The average density of the material from which the coin is made is 9.67 g/cm³.

<h3>Volume of the coin</h3>

The volume of the coin at the given diameter is calculated as follows;

V = Ah

where;

  • A is area of the coin
  • h is the thickness of the coin

V = πd²/4 x h

V = π(2.8)²/4  x (0.21 cm)

V = 1.293 cm³

<h3>average density of the coin</h3>

The average density of the material from which the coin is made is calculated as follows;

density = mass/volume

density = 12.5 g / (1.293 cm³)

density = 9.67 g/cm³

Thus, the average density of the material from which the coin is made is 9.67 g/cm³.

Learn more about average density here: brainly.com/question/1354972

#SPJ1

7 0
2 years ago
What type of electricity comes from an outlet​
zalisa [80]
There’s many types of electricity that comes from an outlet, like [15A, 120 Volt Outlets] those are more common in older homes and can come in two versions [Two-pronged outlet and three-pronged version]
8 0
3 years ago
"Videos of hoverboard riders who were injured when they fell while operating their hoverboards at a low speeds "went viral" over
bagirrra123 [75]

Answer:

The answer is "No, Hoverboards are risky, and riders are in danger of falling".

Explanation:

It's also known as a self-balanced scooter, it handheld electrical devices traveling on two wheels are hoverboards. It dominated the industry around 2015 and since then has become more and more successful. A rider is balanced on a frame between these wheels, driven by battery-powered lithium-ion batteries.

8 0
2 years ago
A sample of nitrogen gas is inside a sealed container. The volume of the container decreases while the temperature is kept const
frez [133]
I guess it’s d) isobaric mate correct me if I am wrong :D
7 0
3 years ago
which pole of a compass needle points north ? please give simple answer with little explaining if any :)
Mumz [18]
I think the North Pole
If I understand this correctly
6 0
2 years ago
Other questions:
  • According to the Hooke’s law formula, the force is proportional to what measurement?
    14·2 answers
  • : The truck is to be towed using two ropes. Determine the magnitudes of forces FA and FB acting on each rope in order to develop
    11·1 answer
  • It's nighttime, and you've dropped your goggles into a 3.2-m-deep swimming pool. If you hold a laser pointer 1.2 m above the edg
    9·1 answer
  • The masses of blocks A and B in the figure (Figure 1) are 20.0 kg and 10.0 kg, respectively. The blocks are initially at rest on
    9·1 answer
  • Write the factors of potential energy
    10·1 answer
  • Explain what happens when a ferromagnetic material is made into a permanent magnet.
    8·1 answer
  • 3. The electric field of a sinusoidal electromagnetic wave has an amplitude of 5.0 V/m. How much radiation energy passes through
    7·1 answer
  • How many planets are in our Solar system?<br> I'll give brainliest
    5·1 answer
  • 8. Why would ChiN want its own currency to be undervalued relative to the U.S. dollar? How does ChiN maintain an undervalued cur
    7·1 answer
  • A solid weighs 0.9N in air and 0.2N in a liquid of density 700kg/m^3. Calculate
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!