1.

In a uniform circular motion, the object is kept along a circular path by a net force acting on it, called centripetal force, which always acts towards the centre of the circular trajectory.

Mathematically, we can write

where F is the centripetal force

m is the mass of the object

As we see from the equation, F (the force) is directly proportional to m (the mass).

2.

The relationship between force (F) and velocity (v) in a uniform circular motion is

where

F is the force

v is the magnitude of the velocity

so, we see that the force is proportional to the square of the magnitude of the velocity, .

Let's also keep in mind that velocity is a vector, so it consists of a direction as well. In a circular motion, the direction of the velocity is tangential to the circular trajectory, while the centripetal force is radial, towards the centre of the circle (so, it is perpendicular to the velocity)

3.

The relationship between the force (F) and the radius (r) in a uniform circular is

and this means that the force is inversely proportional to the radius of the trajectory, r.

4.

Combining the three expressions that we wrote previously, we find a relationship between the centripetal force and all the other 3 quantities:

where

F is the force

m is the mass of the object

v is the tangential speed of the object

r is the radius of the orbit

5.

An equation can be derived if we consider, for instance, the motion of a planet around a star. In that case, the centripetal force is provided by the gravitational attraction between the star and the planet. So we can rewrite F as

where

G is the gravitational constant

M is the mass of the star

m is the mass of the planet in circular orbit around the star

r is the orbital radius of the planet's orbit

v is the speed of the planet

6.

First of all we notice that one term 'm' and one term 'r' can be simplified by the previous equation:

Which can be rewritten as

So in this case the product (GM) represents a constant term, and so the term is constant for every planet orbiting the same star.

7.

The equation can be used in several ways. For instance, it is possible to calculate the orbital speed of a planet revolving around the Sun, by re-arranging the equation as:

where

G is the gravitational constant

M is the mass of the star

r is the orbital radius of the planet's orbit

3. constant - D. a numerical value

2. coefficient - A. the constant preceding the variables in a product

4. expression -E. a mathematical phrase

5. variable - B. a letter... representing an unkown

1. algebraic expression - C. a mathematical expression...

hope this helps

2. coefficient - A. the constant preceding the variables in a product

4. expression -E. a mathematical phrase

5. variable - B. a letter... representing an unkown

1. algebraic expression - C. a mathematical expression...

hope this helps

1. 8+n

2. 4g

3. 2x-5

4. 6/x

5. 3m +9

6. 7+(8-6)

7. If n = 3, 8 - n = 8 - 3

The answer is 5.

8. 18 / 9 = 2

The answer is 2.

9. If x = 4, ten 3x + 1 = 3(4) + 1 = 13

The answer is 13.

2. 4g

3. 2x-5

4. 6/x

5. 3m +9

6. 7+(8-6)

7. If n = 3, 8 - n = 8 - 3

The answer is 5.

8. 18 / 9 = 2

The answer is 2.

9. If x = 4, ten 3x + 1 = 3(4) + 1 = 13

The answer is 13.

Thank you for posting your question. I hope you found you were after. Please feel free to ask me another.

Given mathematical expression means that '9 is a member of the set T'.

Step-by-step explanation:

We are given the mathematical expression,

' 9 € T '.

In words, it means '9 belongs to T'.

That is, 'the element 9 belongs to the set T' i.e. '9 is a member of the set T'.

Hence, the given mathematical expression means that '9 is a member of the set T'.

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