Acceleration

Acceleration is a time rate at which a velocity is changing. As velocity has both magnitude and direction, it is called a vector quantity; acceleration is also a vector quantity and must account for changes in both the magnitude and direction of a velocity. The velocity of a point or an object moving on a straight path can change in magnitude only; on a curved path, it may or may not change in magnitude, but it will always change in direction. This condition means that the acceleration of a point moving on a curved path can never be zero.

If the velocity of a point moving on a straight path is increasing (i.e., if the speed, which is the magnitude of the velocity, is increasing), the acceleration vector will have the same direction as the velocity vector. If the velocity is decreasing (that is, the point or object is decelerating), the acceleration vector will point in the opposite direction. The average acceleration during a time interval is equal to the total change in the velocity during the interval divided by the time interval. The acceleration at any instant is equal to the limit of the ratio of the velocity change to the length of the time interval, as the time interval approaches zero.

When a point moves on a curved path, the component of the acceleration that results from the change in the direction of the velocity vector is perpendicular to the velocity vector and is directed inward, to the concave side of the path; its magnitude is given by the square of the velocity divided by the radius of curvature r of the path: v /r. The change in the magnitude of v may be represented by another vector (that is, a second component of the acceleration) collinear with v and in the same direction if v is increasing and the opposite direction if v is decreasing. If velocity is stated in metres per second, acceleration will be stated in metres per second per second.

Momentum

Momentum is a product of the mass of a particle and its velocity. Isaac Newton's second law of motion states that the time rate of change of momentum is proportional to the force acting on the particle. Albert Einstein showed that the mass of a particle increases as its velocity approaches the speed of light. At the speeds treated in classical mechanics, the effect of speed on the mass can be neglected, and changes in momentum are the result of changes in velocity only.

From Newton's second law it follows that, if a constant force acts on a particle for a given time, the product of force and the time interval (the impulse) is equal to the change in the momentum. Conversely, the momentum of a particle is a measure of the time required for a constant force to bring it to rest.

The momentum of a rigid body is the sum of the momenta of each particle in the body. Being proportional to velocity, momentum has direction; consequently, when a body in plane motion rotates, the momentum of each particle has a moment about any point in the plane. The sum of these moments of momenta is called the angular momentum of the body about the point and is equal to the product of the moment of inertia of the body about the point and the angular velocity of the body. The time rate of change of the angular momentum of a body about a point is equal to the moment of the applied forces about the point. Applied to elementary particles such as electrons, angular momentum is called spin.

Read the text “KEPLER’S LAWS OF PLANETARY MOTION

” and fulfill the tasks given below.