Uniform circular motion is the movement of an object or particle trajectory at a constant speed around a circle with a fixed radius. The fixed radius, r, is the position of an object in uniform or circular motion relative to to the center of the circle. The length of the position vector of the circle does not change but its direction does as the object follows its circular path. In order to find the object’s velocity, one needs to find its displacement vector over the specific time interval. The change in position, or the object’s displacement, is represented by the change in r. Also, remember that a position vector is a displacement vector with its tail at the origin. It is already known that the average velocity of a moving object is ᐃd/ ᐃt, so for an object in circular motion, the equation is ᐃr/ ᐃt. IN other words the velocity vector has the same direction as the displacement, but at a different length. As the velocity vector moves around the circle, its direction changes but its length remains the same. The difference in between two vectors, ᐃv, is found by subtracting the vectors. The average acceleration, a = ᐃv/ ᐃt, is in the same direction as ᐃv, that is, toward the center of the circle. As the object moves around the circle, the direction of the acceleration vector changes, but its length remains the same.One should take note of the fact that the acceleration vector of an object in uniform circular motion always points in toward the center of the circle. Due to this fact, the acceleration of such an object is called center- seeking or centripetal acceleration.

Remember that centripetal acceleration always points to the center of the circle. Its magnitude is equal to the square of the speed, divided by the radius of motion. The equation one must use in order to find the centripetal acceleration of an object in circular motion is a = v²/ r. One way one can measure the speed of an object in circular motion is to measure its period,...

...Uniform CircularMotion – 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 circularmotion 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 circularmotion; 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...

...
E105: UNIFORM CIRCULARMOTION
NADONG, Renzo Norien D.
OBJECTIVE
The purpose of this experiment is to quantify the centripetal force on the body when one of the parameters is held constant and to verify the effects of the varying factors involved in circularmotion. Mainly, horizontal circular type of motion is considered in this activity.
Circularmotion is defined as the movement of an object along the circumference of the circle or the manner of rotating along a circular path. With uniform circularmotion it is assured that the object traversing a given path maintains a constant speed at all times. Centripetal force is a force that tends to deflect an object moving in a straight path and compels it to move in a circular path.
MATERIALS AND METHODS
This experiment was divided into three parts in order to further study and observe the factors that affect the centripetal force of a body. The concept of this experiment is the same on all parts, which is getting the centripetal force given with three different conditions. Every part of the experiment was executed just the same. Mass hanger plus a desired mass of weights were hanged over the clamp on pulley to determine a constant centripetal force which will act as the actual value. But on the third part of this experiment, aside from the centripetal...

...II Uniform CircularMotion
A. Nomenclature
1. Speed – magnitude of an objects rate of motion (no direction, scalar quantity)
2. Velocity – speed and direction of an objects motion (vector, mag & direction)
3. If a car’s speed is constant but direction is changing, velocity is changing.
4. 2 ways to change velocity (change speed or change direction).
5. acceleration – change in speed over time (vector quantity) TWO types;
a. Linear acceleration – speed up or slow down
b. Centripetal acceleration – change direction
B. Centripetal acceleration (ac) – acceleration changes due to change in direction.
1. Centripetal means center seeking
2. ac is always directed toward the center of the curved path (circle)
3. If an object is moving in a circle it will always have a centripetal acceleration
4. ac = v2/r v=velocity tangent to the circle (m/s) r = radius of the circle (m)
C. Centripetal Force – the force that causes and maintains circularmotion
1. Centripetal Force – Fc – psuedo-force (various forces act as center seeking force)
2. Fc – direction always toward the center.
3. Fc=mac (sub ac = v2/r)
4. Identify Fc
a. Rope over your head
b. Car rounds a corner
c. Earth – Moon
d. Gravitron machine (Fn)
e. Loop de loop (Fn Fg)...

...EXERCISE 7 - Rotational Kinematics and circularmotion
1. A wheel has a radius of 4.1 m. How far (path length) does a point on the circumference travel if the wheel is rotated through angles of 30°, 30 rad, and 30 rev, respectively? 2.1m, 1.2x102 m, 7.7. x102m
2. A centrifuge in a medical laboratory rotates at an angular speed of 3 600 rev/min. When switched off, it rotates through 50.0 revolutions before coming to rest. Find the constant angular acceleration of the centrifuge. -226 rad s-2
3. A machine part rotates at an angular speed of 0.60 rad/s; its speed is then increased to 2.2 rad/s at an angular acceleration of 0.70 rad/s2. Find the angle through which the part rotates before reaching this final speed. 3.2 rad
4. A coin with a diameter of 2.40 cm is dropped on edge onto a horizontal surface. The coin starts out with an initial angular speed of 18.0 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular acceleration of magnitude 1.90 rad/s2, how far does the coin roll before coming to rest? 1.02 m
5. A rotating wheel requires 3.00 s to rotate 37.0 revolutions. Its angular velocity at the end of the 3.00-s interval is 98.0 rad/s. What is the constant angular acceleration of the wheel? 13.7 rad s-2
6. It has been suggested that rotating cylinders about 10 mi long and 5.0 mi in diameter be...

...change and the speed (i.e. the magnitude of the velocity) will remain constant.
If a ball is attached to the end of string and swung at a constant speed (i.e. only the direction of the velocity is changing not the magnitude) then there must still be an acceleration. The acceleration is directed towards the center of the motion. This acceleration is call centripetal acceleration!
2.6.2 State the expression for centripetal acceleration.
The acceleration of any object moving in a circle at a constant speed is given by the equation:
(1)
a⃗ =v2r
It is important to note that centripetal acceleration is very special. It is the acceleration required for an object to move in a circle at a constant speed.
The reverse is also true if an object's acceleration is equal to v2r (and perpendicular to the velocity) then the object must be going in a circle.
If an object is moving in a circle at with a changing velocity, then the overall acceleration is not equation to the centripetal acceleration. However the acceleration perpendicular to the velocity (that is the part changing the direction) is still equal to v2r
2.6.3 Identify the force producing circularmotion in various situations
Sometimes people will make reference to the "centripetal force." This is not a real force, its a pseudo-force. In general the centripetal force is made up of many other forces and is the sum of those forces. This is not unlike the idea of a net force...

...Motion
NCERT Chapter Questions and Answers and other Q & A
Q1: An object has moved through a distance. Can it have zero displacement? If yes, support your answer with an example.
Answer: Yes an object can have zero displacement even though it has moved through a distance. It happens when the object moves back to its original position i.e. final position coincides with the starting position.
Example: Suppose an object travels from O to C and then comes back to original position O.
Total distance traveled = actual path covered = OC + CO = 25 + 25 = 50m
Total displacement = shortest distance between final position and initial position = 0m
Q2: What do you mean by a body in rest?
Answer: A body is said to be at rest, if it does not change its position with respect to a fixed point in its surroundings.
Q3: Are motion and rest absolute or relative? Explain with an example.
Answer: No these terms rest and motion are relative. For example, a person inside a car, carrying a ball in his hand will see the ball is at rest. While for another person, outside the car will see the ball is also moving.
Q4: What is meant by scalars and vectors?
Answer:
* Scalar Quantities: Quantities that require magnitudes only to specify them are called scalar quantities or scalars. Mass, length, time, temperature, angle, area, speed, distance, volume and density are examples of scalar quantities.
* Vector Quantities: Quantities...

...ASP 0501
EXERCISES – circularmotion
1 A car travels at a constant speed around a circular track whose radius is 2.6 km. The car goes once around the track in 360 s. What is the magnitude of the centripetal acceleration of the car?
2 An astronaut in a chamber moves on a circular path, much like a model airplane flying in a circle on a guideline. The chamber is located 15 m from the center of the circle. At what speed must the chamber move so that the astronaut is subjected to 7.5 times the acceleration due to gravity?
3. A child is twirling a 0.0120-kg ball on a string in a horizontal circle whose radius is 0.100 m. The ball travels once around the circle in 0.500 s. (a) Determine the centripetal force acting on the ball. (b) If the speed is doubled, does the centripetal force double? If not, by what factor does the centripetal force increase?
4. Car A uses tires for which the coefficient of static friction is 1.1 on a particular unbanked curve. The maximum speed at which the car can negotiate this curve is 25 m/s. Car B uses tires for which the coefficient of static friction is 0.85 on the same curve. What is the maximum speed at which car B can negotiate the curve?
5. A curve of radius 120 m is banked at an angle of 18°. At what speed can it be negotiated under icy conditions where friction is negligible?
6. . A racetrack has the shape of an inverted cone, as the drawing shows. On this surface the cars race...

...Exploration Guide: Uniform CircularMotion
Go to www.explorelearning.com and login. Please type or write your answers on a separate sheet of paper, not squished in the spaces on these pages. When relevant, data collected should be presented in a table.
Objective: To explore the acceleration and force of an object that travels a circular path at constant speed. Motion of this kind is called uniform circularmotion.
Part 1: Centripetal Acceleration
1. The Gizmotm shows both a top view and a side view of a puck constrained by a string, traveling a circular path on an air table. Be sure the Gizmo has these settings: radius 8 m, mass 5 kg, and velocity 8 m/s. Then click Play and observe the motion of the puck.
a. The puck in the Gizmo is traveling at a constant speed, but it is NOT traveling at a constant velocity. Explain why.
b. Because the velocity of the puck is changing (because its direction is changing), the puck must be experiencing an acceleration. Click BAR CHART and choose Acceleration from the dropdown menu. Check Show numerical values. The leftmost bar shows the magnitude of the acceleration, or |a|. (The other two bars show the x- and y-components of the acceleration, ax and ay.) What is the value of |a|? Jot this value down, along with radius = 8 m, so that you can refer to it later.
c. Keeping velocity set to 8 m/s, set radius to 4 m....