<–2/”>a >Rotational Motion
A rotation is a circular movement of an object around a center (or point) of rotation . A three-dimensional object always rotates around an imaginary line called a rotation axis. If the axis passes through the body’s center of mass, the body is said to rotate upon itself, or spin.
A rigid body is a body that can rotate with all the parts locked together and without any change in its shape.
The moment of inertia of a rigid body is given by
I = M K² where M is the total mass of the body and K is called the radius of gyration of the body. The radius of gyration is that distance from the axis of rotation where the whole mass of the body can be assumed to be placed to get the same moment of inertia which the body actually has.Few common Moment of Inertia are given below:-
Rotational Equations governing Rotational Motion are:-
Gravitation is the force by which every mass or particle of matter, including photons, attracts and is attracted by every other mass or particle of matter.The gravitational field at any point P in space is defined as the Gravitational Force felt by a tiny unit mass placed at P.
Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.
Mathematically, this law, and the magnitude of the force due to the gravitational interaction between two particles, is expressed with :-
Properties of Gravitational Force.
It is always attractive in nature while electric and magnetic force can be attractive or repulsive.
It is independent of the medium between the particles while electric and magnetic force depend on the nature of the medium between the particles.
It holds good over a wide range of distances. It is found true for interplanetary to inter atomic distances.
It is a central force i.e. acts along the line joining the centres of two interacting bodies.
It is a two-body interaction i.e. gravitational force between two particles is independent of the presence or absence of other particles.
It is the weakest force in nature : As Fnuclear > F electromagnetic > F gravitational .
It is a conservative force i.e. work done by it is path independent or work done in moving a particle round a closed path under the action of gravitational force is zero.
It is an action reaction pair i.e. the force with which one body (say earth) attracts the second body (say moon) is equal to the force with which moon attracts the earth.
Simple Harmonic Motion
Simple Harmonic Motion is a type of periodic motion or oscillation motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement .
During simple harmonic motion the acceleration is proportional to the displacement x and is oppositely directed. If the displacement is to the right of the equilibrium position, then the acceleration is to the left, and vice versa. The angular speed ? is a constant, a characteristic of the motion. The angular speed can be expressed in terms of the frequency, or the period, of the motion.
Characterstics of SHM:-
It is a motion along a straight line.
The body moves back and forth with respect to a mean position.
The body returns to a given point in the path with the same velocity after regular intervals of time.
The acceleration is directly proportional to its displacement from the mean position and is always directed towards it.
The force acting on the body always tries to bring it back to its equilibrium position.
The maximum displacements on either side of the equilibrium position are equal.,
Rotational motion is the motion of an object around a fixed point. The fixed point is called the axis of rotation. The angular displacement of an object is the angle between its initial and final positions. The angular velocity of an object is the rate at which it changes its angular displacement. The angular acceleration of an object is the rate at which its angular velocity changes. Torque is the force that causes an object to rotate. The rotational inertia of an object is its resistance to changes in its rotation. The moment of inertia of an object is a measure of its rotational inertia. The conservation of angular momentum states that the total angular momentum of a system remains constant unless an external torque acts on the system.
Gravitation is the force of attraction between two objects with mass. The gravitational field is the region of space around an object where a force of gravity is exerted. The gravitational potential energy of an object is the energy it has due to its position in a gravitational field. The escape velocity of an object is the minimum velocity it must have to escape the gravitational pull of a planet or other object. The orbital velocity of an object is the velocity it must have to orbit a planet or other object. Kepler’s laws of planetary motion state that the planets orbit the Sun in elliptical orbits, with the Sun at one focus of the ellipse. The planets sweep out equal areas in equal times. The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.
Simple harmonic motion is a type of periodic motion that occurs when an object is acted upon by a restoring force that is proportional to its displacement from its equilibrium position. The period of a simple harmonic oscillator is the time it takes for the oscillator to complete one cycle of its motion. The frequency of a simple harmonic oscillator is the number of cycles it completes per unit time. The amplitude of a simple harmonic oscillator is the maximum displacement of the oscillator from its equilibrium position. The phase of a simple harmonic oscillator is the angle between its initial position and its current position. A damped harmonic oscillator is a simple harmonic oscillator that experiences a force that opposes its motion. The force of damping causes the amplitude of the oscillator to decrease over time. A forced harmonic oscillator is a simple harmonic oscillator that is acted upon by a periodic force. The periodic force causes the amplitude of the oscillator to increase.
Rotational motion and gravitation are two of the fundamental forces of nature. Rotational motion is responsible for the motion of planets, stars, and galaxies. Gravitation is responsible for the attraction between all objects with mass. Simple harmonic motion is a type of periodic motion that occurs in many systems, such as pendulums, springs, and waves.
1. What is a force?
A force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity.
2. What is work?
Work is the transfer of energy to an object through the application of a force. In physics, work is a scalar quantity that is represented by the letter W. The work done by a force is equal to the force times the distance over which the force is applied.
3. What is energy?
Energy is the ability to do work. It is a fundamental property of the universe that is present in all matter and all fields. Energy can be converted from one form to another, but it can never be created or destroyed.
4. What is power?
Power is the rate at which work is done. It is a scalar quantity that is represented by the letter P. The power of a machine is equal to the work done divided by the time it takes to do the work.
5. What is momentum?
Momentum is the product of an object’s mass and velocity. It is a vector quantity, meaning that it has both magnitude and direction. Momentum is conserved, which means that the total momentum of a system remains constant unless an external force acts on the system.
6. What is angular momentum?
Angular momentum is the rotational equivalent of linear momentum. It is a vector quantity that is equal to the product of an object’s mass, radius, and angular velocity. Angular momentum is conserved, which means that the total angular momentum of a system remains constant unless an external torque acts on the system.
7. What is torque?
Torque is the rotational equivalent of force. It is a vector quantity that is equal to the product of a force and the distance from the point of application of the force to the axis of rotation. Torque is what causes objects to rotate.
8. What is equilibrium?
Equilibrium is a state of balance in which there are no net forces or net torques acting on an object. An object in equilibrium will not change its motion.
9. What is inertia?
Inertia is the resistance of an object to any change in its motion. It is a measure of an object’s mass. The more mass an object has, the more inertia it has.
10. What is acceleration?
Acceleration is the rate at which an object’s velocity changes. It is a vector quantity, meaning that it has both magnitude and direction. Acceleration is caused by a force.
11. What is velocity?
Velocity is the rate at which an object’s position changes. It is a vector quantity, meaning that it has both magnitude and direction. Velocity is equal to the change in position divided by the time it takes to make the change.
12. What is speed?
Speed is the magnitude of an object’s velocity. It is a scalar quantity, meaning that it has only magnitude. Speed is equal to the distance traveled divided by the time it takes to travel the distance.
13. What is distance?
Distance is the total length of the path traveled by an object. It is a scalar quantity.
14. What is time?
Time is a fundamental quantity that is used to measure the interval between events. It is a scalar quantity.
15. What is mass?
Mass is a measure of an object’s inertia. It is a scalar quantity.
16. What is weight?
Weight is the force of gravity on an object. It is a vector quantity. Weight is equal to the mass of an object times the acceleration due to gravity.
17. What is force?
Force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity.
18. What is pressure?
Pressure is the force per unit area exerted by a fluid on a surface. It is a scalar quantity. Pressure is equal to the force divided by the area.
19. What is temperature?
Temperature is a measure of the Average kinetic energy of the
A car is moving at a constant speed of 100 km/h. What is the centripetal force acting on the car?
(A) 0 N
(B) 100 N
(C) 1000 N
(D) 10000 NA satellite is orbiting the Earth at a distance of 1000 km from the center of the Earth. What is the centripetal force acting on the satellite?
(A) 0 N
(B) 100 N
(C) 1000 N
(D) 10000 NA ball is attached to a string and is swinging back and forth. What type of motion is this?
(A) Rotational motion
(B) Gravitational motion
(C) Simple harmonic motionA pendulum is swinging back and forth. What type of motion is this?
(A) Rotational motion
(B) Gravitational motion
(C) Simple harmonic motionA car is driving around a curve. What type of force is acting on the car?
(A) Centripetal force
(B) Centrifugal force
(C) Both centripetal and centrifugal forcesA satellite is orbiting the Earth. What type of force is acting on the satellite?
(A) Centripetal force
(B) Centrifugal force
(C) Both centripetal and centrifugal forcesA ball is attached to a string and is swinging back and forth. What is the restoring force acting on the ball?
(A) The tension in the string
(B) The force of gravity
(C) Both the tension in the string and the force of gravityA pendulum is swinging back and forth. What is the restoring force acting on the pendulum?
(A) The tension in the string
(B) The force of gravity
(C) Both the tension in the string and the force of gravityA car is driving around a curve. What is the net force acting on the car?
(A) 0 N
(B) A force towards the center of the curve
(C) A force away from the center of the curveA satellite is orbiting the Earth. What is the net force acting on the satellite?
(A) 0 N
(B) A force towards the center of the Earth
(C) A force away from the center of the EarthA ball is attached to a string and is swinging back and forth. What is the acceleration of the ball?
(A) The acceleration of gravity
(B) A constant acceleration
(C) An acceleration that changes with timeA pendulum is swinging back and forth. What is the acceleration of the pendulum?
(A) The acceleration of gravity
(B) A constant acceleration
(C) An acceleration that changes with timeA car is driving around a curve. What is the speed of the car?
(A) Constant
(B) Increasing
(C) DecreasingA satellite is orbiting the Earth. What is the speed of the satellite?
(A) Constant
(B) Increasing
(C) DecreasingA ball is attached to a string and is swinging back and forth. What is the period of the ball’s motion?
(A) The time it takes for the ball to make one complete swing
(B) The time it takes for the ball to go from its highest point to its lowest point
(C) The time it takes for the ball to go from its lowest point to its highest pointA pendulum is swinging back and forth. What is the period of the pendulum’s motion?
(A) The time it takes for the pendulum to make one complete swing
(B) The time it takes for the pendulum to go from its highest point to its lowest point
(C) The time it takes for the pendulum to go from its lowest point to its highest pointA car is driving around a curve. What is the radius of the curve?
(A) The distance from the center of the curve to the car
(B) The distance from the center of the curve to the edge of the road
(C) The distance from the center of the curve to the center of the carA satellite is orbiting the Earth. What is the radius of the satellite’s orbit?
(A) The distance from the center of the Earth to the satellite
(B) The distance from the center of the Earth to the edge of the satellite’s orbit
(C) The distance from the