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Even Numbers

First value in the sequence of even numbers:

Amount of even numbers:

This symbol is placed between the even numbers in output:

Direction of Growth:
Increasing Even Numbers
Decreasing Even Numbers

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Generate an Arithmetic Progression >

Quickly create a list of numbers in arithmetic series.

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Quickly create a list of numbers in geometric series.

Draw Pascal's Triangle >

Quickly calculate the coefficients of the binomial expansion.

Convert Numbers to a Picture >

Quickly create a downloadable image from numbers.

Generate Random Numbers >

Quickly create a list of random numbers.

Generate Random Prime Numbers >

Quickly create a list of random primes from a specific interval.

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Quickly create a matrix with random numbers as its elements.

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Find the Transpose of a Matrix >

Quickly exchange rows and columns of a matrix.

Find Matrix Inverse >

Quickly find the inverse matrix of any square matrix.

Calculate Matrix Determinant >

Quickly find the determinant of any square matrix.

Calculate Pi Digits >

Quickly calculate any number of digits of number π.

Random Prime Numbers

7027\n5441\n3487\n7687\n4567\n6079\n9931\n8689\n53\n9743

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Time left: 10:00

Time Left: 10:00

Question 1: A disc is rotating with an angular velocity of 20 rad/s. What is its angular displacement after 2 seconds?

20 rad
30 rad
40 rad
50 rad

Question 2: The moment of inertia of a body depends on:

Its linear velocity
Distribution of mass and axis of rotation
Both of the above
None of the above

 

Question 3: If a particle moves in a circular path with uniform speed, its:

Angular velocity is constant
Tangential acceleration is constant
Radial acceleration is zero
None of the above

Question 4: A flywheel has a moment of inertia of 10 kg·m² and is rotating at 100 rad/s. What is its rotational kinetic energy?

100 J
500 J
1000 J
50000 J

Question 5: Which of the following quantities is a vector?

Angular speed
Angular velocity
Rotational kinetic energy
Moment of inertia

Time Left: 10:00

Question 1: A disc is rotating with an angular velocity of 20 rad/s. What is its angular displacement after 2 seconds?

20 rad
30 rad
40 rad
50 rad

Question 2: The moment of inertia of a body depends on:

Its linear velocity
Distribution of mass and axis of rotation
Both of the above
None of the above

Question 3: If a particle moves in a circular path with uniform speed, its:

Angular velocity is constant
Tangential acceleration is constant
Radial acceleration is zero
None of the above

Question 4: A flywheel has a moment of inertia of 10 kg·m² and is rotating at 100 rad/s. What is its rotational kinetic energy?

100 J
500 J
1000 J
50000 J

Question 5: Which of the following quantities is a vector?

Angular speed
Angular velocity
Rotational kinetic energy
Moment of inertia

Time Left: 10:00

Question 1: A disc is rotating with an angular velocity of 20 rad/s. What is its angular displacement after 2 seconds?

20 rad
30 rad
40 rad
50 rad

Question 2: The moment of inertia of a body depends on:

Its linear velocity
Distribution of mass and axis of rotation
Both of the above
None of the above

Question 3: If a particle moves in a circular path with uniform speed, its:

Angular velocity is constant
Tangential acceleration is constant
Radial acceleration is zero
None of the above

Question 4: A flywheel has a moment of inertia of 10 kg·m² and is rotating at 100 rad/s. What is its rotational kinetic energy?

100 J
500 J
1000 J
50000 J

Question 5: Which of the following quantities is a vector?

Angular speed
Angular velocity
Rotational kinetic energy
Moment of inertia

Rotational Motion Quiz

Time left: 10m 0s

1. What is the moment of inertia of a solid sphere of mass M and radius R about its diameter?

(2/3) MR²
(1/2) MR²
(2/5) MR²
(3/5) MR²

2. What is the angular velocity of an object rotating with a period of 2 seconds?

π rad/s
2π rad/s
π/2 rad/s
4π rad/s

3. What is the relationship between torque (τ) and angular acceleration (α) for a rigid body?

τ = Iα²
τ = Iα
τ = α/I
τ = I²α

4. A disk is spinning with an angular velocity ω. If the radius of the disk is doubled, how does the moment of inertia change?

It remains the same
It doubles
It halves
It quadruples

5. Which of the following quantities is conserved in a system with no external torque?

Linear momentum
Kinetic energy
Angular momentum
Potential energy

Rotational Motion Quiz

Time left: 10m 0s

1. What is the moment of inertia of a solid sphere of mass M and radius R about its diameter?

(2/3) MR²
(1/2) MR²
(2/5) MR²
(3/5) MR²

2. What is the angular velocity of an object rotating with a period of 2 seconds?

π rad/s
2π rad/s
π/2 rad/s
4π rad/s

3. What is the relationship between torque (τ) and angular acceleration (α) for a rigid body?

τ = Iα²
τ = Iα
τ = α/I
τ = I²α

4. A disk is spinning with an angular velocity ω. If the radius of the disk is doubled, how does the moment of inertia change?

It remains the same
It doubles
It halves
It quadruples

5. Which of the following quantities is conserved in a system with no external torque?

Linear momentum
Kinetic energy
Angular momentum
Potential energy