Uniform Circular Motion – a constant motion along a circle; the unfirom motion of a body along a circle
Frequency (f) – the number of cycles or revolutions completed by the same object in a given time; may be expressed as per second, per minute, per hour, per year, etc.; standard unit is revolutions per second (rev/s)
Period (T) – the time it takes for an object to make one complete revolution; may be expressed in seconds, minutes, hours, years, etc.; standard unit is seconds per revolution (s/rev)
Note: Period and frequency are reciprocals: T = 1/f; f = 1/T.
1. Suppose the rear wheel makes 5 revolutions in 1 minute. Find the wheel’s period and frequency. 2. As a bucket of water is tied to a string and spun in a circle, it made 85 revolutions in a minute. Find its period and frequency. 3. * An object orbits in a circular motion 12.51 times in 10.41 seconds. What is the frequency of this motion?
Tangential Speed (v or vs) – average speed; rotational speed; speed of any particle in uniform circular motion; standard unit is meters per second (m/s); v = Cf = C/T = 2πrf = 2πr/T = rω
3. What is the rotational speed of a person standing at the earth’s equator given that its radius is 6.38*106 m and that it takes 365 days for the earth to complete a revolution? 4. A ball that is whirled about on a string makes 167 revolutions in 3 minutes. If the string is 1.5 meters long, find the average speed of the ball. 5. * A stone tied on a rope has a frequency of 27 rpm. Find the average speed of the stone if the rope is 12 meters long.
Centripetal Acceleration (ac) – the rate of change of tangential velocity; standard unit is meters per square second (m/s2); ac = v2/r = vω
5. A metal ball is attached to a 1-m long string and is whirled to make 3 revolutions per second with the other end as the center. How much acceleration will the metal ball experience?
Centripetal Force (Fc) – the net force causing the centripetal acceleration of an object in circular motion; standard unit is Newton (N) or kgm/s2; Fc = mac = (mv2)/r = 4π2f2mr = mrω2 = W(tanϴ)
Note: As a car makes a turn, the force of friction acting upon the turned wheels of the car provides centripetal force required for circular motion. As a bucket of water tied to a string is spun in a circle, the tension force acting upon the bucket provides the centripetal force required for circular motion. As the moon orbits the earth, the force of gravity acting upon the moon provides the centripetal force required for circular motion.
6. A 20000-kg vehicle is running at 80 km/h in a rotunda with a radius of curvature 25 m. Compute for the centripetal force and acceleration.
1. An object orbits in circular motion 12.51 times in 10.41 seconds. What is the frequency of this motion? 2. A stone tied on a rope has a frequency of 27 rpm. Find the average speed of the stone if the rope is 12 m long. 3. An amusement park ride whirls you in a horizontal circle with radius of 7.00 m. How fast must you be going to experience a horizontal acceleration of twice the acceleration due to gravity? 4. Compute for the centripetal force and acceleration of an electron orbiting a single proton (in the Bohr model of a hydrogen atom) given that the electron is orbiting around the proton at a distance of 5*10-11 m and at a speed of 2*105 m/s.
Friction Force (f) – a force that tends to oppose motion; exists when two boes are in contact; standard unit is Newton (N); f =usFN
Normal Force (FN) – the force perpendicular to the surface of contact;standard unit is Newton (N); FN = f/us = W = mg = mg(cosϴ) (inclined from the horizontal)
Rotational Motion – the motion of a body turning about its axis
Angular Displacement (ϴ) – the angle through which an object has rotated; expressed in radians (rad); ϴ = s/r where s represents arc length and r represents radius
Note: 1 rev = 2π rad = 360°; 1...
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