Practice Questions

A couple is a pair of forces of equal magnitude but acting in opposite directions with different lines of action that produces rotation without translation. The couple produced by a pair of forces is a rotational motion and not a translational motion.

Combination of translatory and rotational

Impulse is the change in momentum caused by a force during a specific time interval. It is measured as the total effect of force and is a vector quantity with the same direction as the force. Impulse is equal to the force multiplied by time and its Sl unit is Newton-second or kg - m - s ^ - 1

moving car possesses both kinetic energy of translation and rotation. Kinetic energy is the energy possessed by a body due to its motion. The formula for kinetic energy is $KE = 1/2 mv ^ 2$ where m is the mass of the body and v is the velocity of the body. As the car has rotating wheels, it also possesses rotational kinetic energy ($1/2 I \omega ^ 2$) Where I = Moment of inertia, omega = angular velocity of the wheel

kinetic energy of translation and rotation

D'Alembert's principle states that the sum of the differences between the forces acting on a system and the time derivatives of the momenta of the system, projected onto any virtual displacement consistent with the constraints of the system, is zero. In practical terms, it's used to reduce problems in dynamics to equivalent static problems.

reduction of problems of dynamics to equivalent statics problem

Rotation is the process of turning. Examples of rotational motion include the spinning of the earth, a fan moving in a house, and a group of people holding hands and walking in the same direction.

The observation of a fan continuing to move after being switched off illustrates Newton's First Law of Motion, which states that a body will remain in its state of rest or uniform motion in a straight line unless acted upon by an external force. This law applies when there is no net external force on the body

The principle of conservation of momentum

he rate of change of momentum of a body is directly proportional to the net force acting on it, as given by the equation F = d/dt (P) Therefore, the direction of the change in momentum takes place in the direction of the applied force.

Opposite to the direction of applied force

A satellite is kept on moving in its orbit around the earth due to the centripetal force. This force acts on a body moving in a circular path and is directed towards the centre around which the body is moving. It is caused by the gravitational attraction between the Earth and the satellite.

Rate of change of momentum is directly proportional to the impressed force. This is stated in Newton's Second Law of Motion. Mathematically, F = d/dt (P) = d/dt (mv) = ma

When a body falls freely under gravitational force, it possesses no weight. The apparent weight of the body moving downward with acceleration (a) is given by m(g-a). Under free fall condition, a = g, thus the apparent weight becomes 0.

Newton's first law of motion, also known as the law of inertia, states that an object at rest or in uniform motion will continue to be so until acted upon by an external force. This law implies that a force is required to cause a change in motion.

Newton's second law of motion explains the measure of a force and establishes the fundamental equation of dynamics, which states that the rate of change in linear momentum of a body is directly proportional to the external force applied to the body and this change takes place always in the direction of the applied force. The equation for this law is F = ma where F is the force, m is the mass and a is the acceleration.

Newton's law of gravitation states that the force between two particles is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The equation for this is$F \propto {\frac {m_1 m_2}{ r^ 2}} \Rightarrow F = G \frac {Mm}{r ^ 2}$ where G is the gravitational constant.

Directly proportional to square of distance

Inversely proportional to square of distance

Directly proportional to fourth power of distance

Inversely proportional to fourth power of distance

Newton's third law of motion
every action there is an equal and opposite reaction

according to Newton's second law of motion F = ma

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