Reviewer for Uniform Circular Motion
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.
Sample Problems:
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
Sample Problems:
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
Sample Problem:
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
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.
Sample Problems:
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
Sample Problems:
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
Sample Problem:
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