Lectures in Physics
ENGR. HAROLD JAN R. TERANO, ECE
ROTATIONAL KINEMATICS AND DYNAMICS
Uniform Circular Motion – an object moves at a constant speed along a circular path.
Velocity is always tangent to the path in circular motion. Speed is constant, velocity is not.
Centripetal Acceleration, – acceleration that maintains the object along a circular path directed towards the center. Also called as radial acceleration. In 1673, Christian Huygens, determined the following relationships. Velocity, Where, r = radius of curvature/path, t = time/period.
Frequency (f) – number of revolutions of cycle completed per unit time. So,
Expressing centripetal acceleration in terms of frequency,
In terms of period,
Example(1) It takes a merry-go-round moves 30 seconds to complete one revolution, what is the velocity of the child on top of a horse found 3 meters away from the center?
r = 3 meters t = 30 seconds
v = ?
Example(2) A micro compact disc (CD) is 6 cm in diameter. If a drive spins uniformly at 300 revolutions per minute, what is the acceleration in m/s2 of a particle of dirt found along the edge?
d = 6 cm f = 300 rev/min.
ac = ?
Centripetal and Centrifugal Forces
Centripetal Force – is the force (real force) on the body towards the center of rotation when a body is moving around a curved path.
Centrifugal Force – is the force (apparent force) on the body directed away from the center of rotation when a body is moving around a curved path.
Where, m = mass in kg, VT = tangential velocity in m/s, r = radius of curvature
Example(1) An automobile weighs 1500 kg. If this car is driven around a curve, which has a radius of 250 m at the rate of 45 m/s, what is the centripetal force of the road on the