# Lectures in Physics

**Topics:**Kinematics, Velocity, Classical mechanics, Force, Acceleration /

**Pages:**4 (761 words) /

**Published:**Jan 29th, 2013

Lecture Notes

Prepared by:

ENGR. HAROLD JAN R. TERANO, ECE

Lesson 5

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?

Given:

r = 3 meters t = 30 seconds

Req’d:

v = ?

Solution:

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?

Given:

d = 6 cm f = 300 rev/min.

Req’d:

ac = ?

Solution:

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