Skip to content
StickMan Physics

StickMan Physics

Animated Physics Lessons

Menu
  • Home
    • Stickman Physics Music: Blending Science with Sound
    • Unit 1: One Dimensional Motion: Physics Introduction
    • Unit 2: Two Dimensional Motion: Projectile and Non-Projectile
    • Unit 3: Newton’s Laws of Motion and Force
    • Unit 4: Universal Gravitation and Circular Motion
    • Unit 5: Work, Power, Mechanical Energy, and Simple Machines
    • Unit 6: Momentum Impulse and Conservation of Momentum
    • Unit 7: Electrostatics
    • Unit 8: Current and Circuits
    • Unit 9: Magnets and Magnetism
    • Unit 10: Waves
    • Unit 11: Electromagnetic Waves
    • Unit 12: Nuclear Physics
  • Table of Contents
  • Practice
  • Equation Sheet
  • Digital Learning
  • Contact
Menu

Circular Motion

Circular Motion

Circular motion requires an inward force, centripetal force, to create a change in direction resulting in a circular pattern.

Go through this lesson with our video or read and do the practice checking your work with our solutions below.

Two Types of Circular Motion

A rotation occurs when an entire object spins around an internal axis.  A revolution is when an object is located beyond the axis and follows a circular path around beyond the axis.  See how the stickman is revolving around the central axis.  The axis is a central point around which rotation takes place.

rotation revolution

Tangential Velocity

The tangent is a straight line that would just touch the curve of the circle as seen in the animation.

Because velocity is a vector, it includes magnitude and direction.  So will use the term tangential velocity to represent what the velocity would be if released and allowed to follow a straight line path.

tangential velocity

Inertia Versus Circular Motion

  • Inertia makes an object want to continue forward at a constant velocity
  • We need a inward force to change direction and create circular motion
  • This inward force is centripetal force (Fc)
inertia versus circular motion

Centripetal Force

Centripetal Force (Fc) is an inward force towards the center of a circle, changing the direction, keeping an object in a circular path.

Since direction changes due to centripetal force, circular motion is accelerated and we call this centripetal acceleration (ac).

If you lost the centripetal force the object would stop revolving and continue in a straight line tangent to the circumference of the circle.

inertia without centripetal force

Q4: What would happen to a rubber stopper in circular motion if there were no centripetal force?

It would move straight ahead tangent to the circumference of the circle

Q5: What is tangential velocity?

Velocity straight ahead from the circumference of a circle

Q6: What force is necessary to have circular motion?

Centripetal Force

Q7: What direction is this force?

Towards the center of the circle

Q8: A moving object’s inertia make it want continue ______________________________.

Straight ahead at a constant velocity

Circular Motion Variables

VariableNameUnitUnit Abbreviation
Fccentripetal forceNewtonN
mMasskilogramkg
accentripetal accelerationmeters per second squaredm/s2
v or vtangentialvelocity or tangential velocitymeters per secondm/s
rradiusmetersm
Tperiodsecondss
ffrequencyhertzHz

 

Centripetal Force Causes Centripetal Acceleration

Centripetal force creates centripetal acceleration related to mass is seen in this equation:

centripetal force acceleration equation

Centripetal acceleration is equal to the velocity squared divided by the radius seen in this equation:

centripetal acceleration equation

Q9: How much centripetal force is required to create an inward acceleration of 2.0 m/s2 to keep a 0.60 kg object in a circular path?

Q9

Q10: What is the velocity of an object going in a circle that has a radius of 1.2 meters and an inward acceleration of 4.5 m/s2?

Q10

The result after putting the previous two equations together is this main centripetal force (Fc) equation

Centripetal Force Equation

Q11: How much centripetal force is required to cause a 21 kg object to rotate with a speed of 5.0 m/s in a circle with a radius of 1.0 meters?

Q11

Sources of Centripetal Force

What provides the centripetal force allowing for circular motion?

Friction for a car to drive around a corner

      • Fc = Ff friction

Gravity for the moon to go around earth

      • Fc = Fg gravity

Tension for spinning something around your head with a rope

      • Fc = FT tension in the rope
types of centripetal force

Important Note: The problems in this unit may not state centripetal force directly.  They may ask what is the tension, gravity, or friction keeping an object in circular motion.  If stated this way, solve for centripetal force (Fc).

What is a Period?

Period (T) is the time it takes for a specific motion to occur.  See in the animation how this could be one swing, rotation, wave, segment, or osculation.  In this unit it will be a rotation.

period

Period and Frequency

  • Period (T) is the time it takes for one cycle and has the unit second (s)

Period Equation

frequency equals time divided by number of cycles

  • Frequency (f) is the number of cycles per time and has the unit Hertz (Hz) which also means cycles per second

Frequency Equation:

period equals cycles divided by time

You can find either period or frequency with number of cycles and time that those took or with inverse of  frequency or period.

period and frequency are inverse of each other

period and frequency

Q12: What is the period when 50 rotations occur in 20 seconds?

Q12

Q13: What is the frequency when 50 rotations occur in 20 seconds?

You can now solve this two ways after doing question 13

Q13

Tangential Velocity Equation

Tangential velocity is calculated by taking the circular distance divided by the time it takes to go around the circle or period (T).  The distance around the circle is found by calculating the circumference of a circle.

2πr = circle circumference (unit: meters (m))

T = Period: Time it takes for one rotation (unit: seconds (s))

 

tangental velocity

A greater radius gives an object a greater velocity when having the same period.  You can analyze the equations in this unit along with any other using the rule of ones.  Click here if you want a reminder on how to use this.  Notice in the image that the fastest circle is green which is the furthest out and the slowest is red.

greater radius greater tangental velocity

Q14: What is the tangential velocity of a carnival ride that takes 5.0 seconds to go around in a circle with a radius of 20 meters?

Q14

Q15: Does tangential velocity increase or decrease when further away from the axis on a rotating object?

Q15

Q16: How much different is the tangential velocity if an object takes three times as much time to revolve around an object at the same radius?

Q16

Centripetal Force Example Problems

1. What would happen to the centripetal force required to keep an object going in a circle if the radius of a circle was doubled?

1

2. How many times the centripetal force would you have if a car slowed from 60 mph to 20 mph going around a curve?

2

3. Kent spins in his chair with a frequency of 0.5 Hz. What is the period of his spin?

F = 0.5 Hz

T = 1/f =1/0.5 = 2 s

(Click on the picture to enlarge it)

4. A record takes 1.3 s to make one complete rotation. An object on this record is 0.12 m from the center.  What is its velocity?

4

5a. The pilot of a 60,500 kg jet plane is flying in circles whose radius is 5.00 x 104 m.  It takes 1.8 x 103 s to make one rotation.  What is the velocity of the plane?

5a

5b. How much centripetal force would there be?

5b

6. What is the centripetal acceleration of a bike traveling a tangential speed of 8 meters per second in a circle that has a radius of 5 meters?

6

Circular Motion Practice Quiz

2408

Circular Motion Quiz

1 / 10

What happens to tangential velocity if you increase the radius?
It _________

velocity tangential

2 / 10

The time it takes for one rotation is the ___________.

The period is the time it takes for an event that occurs over and over to happen.  In this case it is time to travel in a circle

3 / 10

The number of rotations per time is the ___________.

Frequency is the number of rotations per time and its unit is Hz or rotations per second

4 / 10

The inward force that causes circular motion is _________________.

Inertia makes an object want to go forward at a constant rate if in motion.  Centripetal force pulls that object inwards making its motion circular.

5 / 10

ball on string

How would a ball travel if you were spinning a ball on a rope above your head and the rope broke?

The ball will keep on going straight when there is not a centripetal force pulling it in.  Straight from the outside of the circle is called tangent.  So it would go straight ahead tangent to the circle.

6 / 10

Why would a coffee cup sitting on your car fall off when taking a quick a turn?

Its inertia makes it keep on going forward as the car is turning

7 / 10

What will happen to the centripetal force required to keep an object going in a circle if the mass of the object is doubled and the radius of the circle is cut in half?

It would become ___________ times the original.

Circular Motion

8 / 10

What will happen to the centripetal force required to keep an object going in a circle if mass, radius, and velocity are all doubled?

It would become ___________ times the original.

circular motion 1

9 / 10

What is the tangential velocity of a 50 kg girl is bicycling in circles with a radius of 5.00 m when it takes 12 s to make one rotation?

tangential velocity

10 / 10

What is the centripetal force of a 50 kg girl is bicycling in circles with a radius of 5.00 m when it takes 12 s to make one rotation?

Circular Motion

Your score is

LinkedIn Facebook Twitter
0%

Links:

  • On to our StickMan Physics Torque Page
  • Back to the main Universal Gravitation and Circular Motion Page
  • Back to the Stickman Physics Home Page
  • Equation Sheet

StickMan Physics Logo  StickMan Physics Home

Stickman Physics Music Page

Unit 1: One Dimensional Motion
Unit 2: 2D Motion
Unit 3: Newton’s Laws and Force
Unit 4: Universal Gravitation and Circular Motion
Unit 5: Work, Power, Mechanical Advantage, and Simple Machines
Unit 6: Momentum, Impulse, and Conservation of Momentum
Unit 7: Electrostatics
Unit 8: Current and Circuits
Unit 9: Magnetism and Electromagnetism
Unit 10: Intro to Waves
Unit 11: Electromagnetic Waves
Unit 12: Nuclear Physics

AP Physics 1 Pages (Deeper Dive into Concepts)

DIY Creations for Fun and Physics

Teachers: Do you want lessons and handouts already put together?  Find resources at TeachersPayTeachers.

©2025 StickMan Physics | Built using WordPress and Responsive Blogily theme by Superb

Terms and Conditions - Privacy Policy