DEC 1013 ENGINEERING SCIENCES. 13. CENTRIPETAL AND CENTRIFUGAL FORCE. NAZARIN B. NORDIN [email protected] What you will learn:. Centripetal force: acceleration, centrifugal force/ acceleration, mass-radius polygons Centrifugal force applied to wheel balancing/ clutches, governors
13. CENTRIPETAL AND CENTRIFUGAL FORCE
NAZARIN B. NORDIN
6 segments gets
One radian is the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.
2p segments gets completely around.
1 rev = 3600 = 2p radians (rad)
Thus the angle q in radians is given in terms of the arc length l it subtends on a circle of radius r by
The radian measure of an angle is a dimensionless number.
The angular speed (w ) of an object whose axis of rotation is fixed is the rate at which its angular coordinate, the angular displacement q, changes with time. If q changes from qi to qf in a time t, then the average angular speed is
The units of a are typically rad/s2, rev/min2, and such.
It is possible to associate a direction with w, and therefore with a, thereby specifying the angular acceleration vector a, but we will have no need to do so here.
Equations for uniformly accelerated angular motion are exactly analogous to those for uniformly accelerated linear motion. In the usual notation we have:
Uniform Circular Motion
An object moving in a circle with constant speed, v, experiences a centripetal acceleration with:
*a magnitude that is constant in time and
is equal to
*a direction that changes
continuously in time and
always points toward the
center of the circular path
For uniform circular motion, the velocity is tangential to the circle and perpendicular to the acceleration
Period and Frequency
A circular motion is described in terms of the period T, which is the time for an object to complete one revolution.
The distance traveled in one revolution is
The frequency, f, counts the number of revolutions per unit time.
Example of Uniform Circular Motion
The moon’s nearly circular orbit about the earth has a radius of about 384,000 km and a period T of 27.3 days. Determine the acceleration of the Moon towards the Earth.
Uniform Circular Motion
Newton’s 2nd Law: The net force on a body is equal to the product of the mass of the body and the acceleration of the body.
*The centripetal accelerationis caused by a centripetal force that is directed towards the center of the circle.
An object rotating about an axis tends to remain rotating at the same rate about the same axis unless interfered with by some external influence.
The sluggishness of an object to changes in its state of rotational motion
Because v = rw, we also have
where w must be in rad/s.
The centripetal force (Fc) is the force that must act on a mass m moving in a circular path of radius r to give it the centripetal acceleration v2/r. From F = ma, we have
Where Fc is directed toward the center of the circular path.