Circular Motion. Pearson 2007-2008. 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
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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.
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.
*So we find thatamoon/ g = 0.000278
*Newton noticed thatRE2 / R2= 0.000273
*This inspired him to propose that Fgravity 1 / R2 (more on gravity in future lectures)
*motion in a circle or circular arc at constant speed
*the acceleration changes the direction of the velocity, not the magnitude
*the “center-seeking” orcentripetal accelerationis always orthogonal to the velocity and has magnitude:
The period of
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.
Does the contact force between the wine glass and red-water remain constant in uniform circular motion?
The water doesn’t fall because the centripetal force on the water cancels the force of gravity.
The water doesn’t fall because there isn’t enough time for it to fall.
The water doesn’t fall because of the horizontal force applied to it by the glass, plus friction with the glass.
The water is falling, but the glass is falling faster than it would under free fall.
mac = mv2/r = mg + Ny
ac = g N/m
When N=0, the centripetal acceleration is just g.
What speed is needed to lose contact between wine glass and red-water?
(1) Top statement:
*as q 90, v increases.
*v is independent of mass.
mgDemo 1D-2 Conical Pendulum
The period, T, is independent of mass and depends only on H.
A car of mass, m, is traveling at a constant speed, v, along a flat, circular road of radius, R. Find the minimum µs required that will prevent the car from slipping
A mass, m, on a frictionless table is attached to a hanging mass, M, by a cord through a hole in the table. Find the speed with which m must move in order for M to stay at rest.
N mass, M, by a cord through a hole in the table. Find the speed with which m must move in order for M to stay at rest.
A car of mass, m, is traveling at a constant speed, v, along a curve that is now banked and has a radius, R. What bank angle, q, makes reliance on friction unnecessary?
An airplane is flying in a horizontal circle with a speed of 480 km/hr. If the wings of the plane are tilted 40o to the horizontal, what is the radius of the circle in which the plane is flying? (Assume that the required force is provided entirely by an “aerodynamic lift” that is perpendicular to the wing surface.)