Uniform Circular Motion (UCM)



Uniform Circular Motion (UCM) General Physics

Class Activity: Investigating the Motion

Objective: Investigate how forces acting on an object affect the motion of the object.

Materials: marble, a circular pathway, your skills of observation.

Procedure: Follow the instructions for each scenario. Record your observations.

1. Roll the marble across the lab table.

a. What are your observations? Does the marble speed up, slow down or move at constant speed? Does it roll in a straight line or in a curve? (If your marble is not rolling in a straight line, try another spot – this observation is best done on a level surface.)

b. Draw a diagram of the rolling marble, and the forces acting on the marble as it rolls.

c. Are the forces balanced or unbalanced?

2. Roll the marble on the circular pathway (provided on a separate sheet of paper). If you want your marble to roll in a circular pathway, what must you do?

Figure out what you all must do to keep the marble rolling in a circular pathway.

a. Record your observations and describe how you did it.

b. What kind of force caused the marble to roll in a circle?

c. Which direction is the marble being pushed?

d. What happens to the pathway of the marble if you stop pushing it in a circle?

Uniform Circular Motion (UCM) General Physics

Review Questions:

• What are Newton’s first two laws of motion?

• What would a moving object do if the forces acting on it were balanced?

• What does acceleration mean?

• What happens to objects when they accelerate?

• What causes objects to accelerate?

Uniform Circular Motion

(UCM) occurs when an object moves at constant speed in a circular pathway.

The speed remains constant, but the velocity does not, because the object's direction is always changing (velocity = speed + direction) .

Since the direction component of velocity is changing as the object moves in a circle, the object is accelerating. It is called centripetal acceleration (ac), and it measures how quickly the object is changing direction.

• What causes an object to accelerate???

The unbalanced force (net force) that causes objects to move in a circle is called the centripetal force (FC). The centripetal force is provided by a real force acting on the object, and it pulls or pushes the object toward the center of the circular pathway, always changing the direction the object is moving.

• What kind of REAL FORCES push or pull objects in circular pathways?

The Centripetal Force is a center pointing force that causes the object to change direction. Centripetal forces are provided by REAL FORCES acting on the object. (FT, Ff, FN, Fg)

(The actual force acting on the object

that causes it to change direction.)

Situation Centripetal Force Provider

Object on a string or wire

swinging in a circle

Object in a circular drum

or on a circular track

Object going around a curve

Object orbiting another object

What is the centripetal force provider in each situation?

Situation: Observation: What is pushing or pulling the object?

(What kind of force is causing the object to change direction?)

A ball is tied to a string and twirled in a circle

Tetherball on a pole

A child swings on amusement park swings

A ball rolls around a circular pathway in a wooden hoop

A ball rolls around a vertical circular track (like a roller coaster)

Salad in a salad spinner

Water in a bucket swinging in a circle

object on a tray swinging in a circle

clothes in a washing machine

object on a rotating platform

car going around a curve (exit ramp)

Children playing on a merry-go-round

a satellite orbiting the Earth

the moon orbiting the Earth

• A ball is whirled in a circle on the end of a string.

Which direction will the ball go if the string is let go?

• A bowling ball is swept in a circular pathway by

physics students. Which direction does the ball

go if a student is not touching the ball?

The direction of the velocity of an object in UCM is always changing and is tangent to the pathway at each moment. Provide some examples and diagrams!

Drawing a free body diagram for UCM:

Fc always points toward

ac always points toward

velocity is

Uniform Circular Motion (UCM) (continued) General Physics

When an object moves in a circle, they can repeat the same pathway over and over again. We say that it is uniform if….

Once around a circular pathway is called a revolution.

The circumference (C = 2πr)

The period (T)

• How do you find the speed/velocity of an object?

How do you calculate the speed of an object moving in Uniform Circular Motion??

• Velocity (v) (magnitude only = speed)

• Acceleration (ac)

• Centripetal Force (Fc)

Example Problem: A red buggy moves in a circle on the front desk.

How fast is it moving?

What is the centripetal acceleration of the buggy?

Equations in this unit….

v = d v = 2πr ac = v2 Fc = mac Fc = m v2

t T r r

Practice Problems: For each problem, draw a diagram of the object moving in a circle. Draw in arrows to show the direction of the centripetal force, the centripetal acceleration and the velocity. Make a table of variables identifying the giving quantities and the units. Writhe the equation, substitute values into the equation and record the answer with the correct units.

1. A 0.5 kg mass is attached to the end of a 1.5 m string. The mass is whirled in a horizontal circle. The stopper completes each revolution in 0.5 sec. Find the velocity of the rubber stopper as it moves in a circle. What kind of force causes the mass to move in a circle?

2. The Barf-with-Bunning ride at Magic Mountain has a radius of 5 m and spins with a period of 3.1 s. What is the speed of the occupants of the ride? What acceleration do they experience? What force does Ben (60 kg) experience as he goes on the ride? What kind of force causes the occupants to move in a circle? (10.1 m/s; 20.4 m/s2; 1224 N)

3. How long does it take for a piece of lettuce to go one time around a salad spinner that has a radius of 0.20 m that is moving at 15 m/s? What is the centripetal force provider? (.08 sec; FN)

Uniform Circular Motion Class Work/Homework Problems

Draw a diagram of the object in each situation. Include arrows that represent the direction of the centripetal force (FC) the centripetal acceleration (ac) and the velocity (v).

1. A .025 kg ball on a 0.5 m string completes a revolution in 0.4 seconds.

a. How far does the ball go in one revolution (circumference of the circle)?

b. What is the speed of the ball?

c. Find the centripetal acceleration of the ball.

d. Find the FT acting on the ball.

2. A 40 kg child sitting 1.1 m from the center of a merry -go-round moves in a circle at a constant speed of 1.25 m/s.

a. Calculate the centripetal acceleration acting on the child.

b. What kind of force is the centripetal force provider?

c. Find the force of friction exerted on the child.

3. A 0.7 kg toy car drives through a portion of a horizontal, circular track. It moves through one half of a circle with a radius of 2 meters in 3 seconds.

a. What actual force allows the car to travel in a circular path?

Find: b. the distance the car traveled around the curve (half the circumference of the circle)

c. the linear velocity (speed) of the car

d. ac of the car

e. Fc on the car

4. The moon's nearly circular orbit about the Earth has a radius about 3.84 x 108 m. What kind of force keeps the moon in orbit? If the moon slowed down or stopped moving, what would happen?

Reference Table: Uniform Circular Motion

| |aC = centripetal acceleration |

|C = 2πr |C = circumference |

| |F = force |

|v = d/t so… in a circle v = C/T |FC = centripetal force |

| |Ff = force of friction |

|aC = v2/r |Fg = force of gravity or weight |

| |FN = normal force |

|FC = m aC |Fnet = net force (unbalanced force) |

| |FTen = force of tension |

|FC = m v2/r |g = acceleration due to gravity (9.8 m/s2 on Earth) |

| |m = mass |

|Fg = mg |r = radius |

| |t = time |

| |T = period |

| |v = velocity |

Driving on Curved Roadways UCM Conceptual Physics

1. What kind of force keeps a car moving in a curved pathway? What kinds of factors affect the size of that force?

2. What direction does the force act?

3. Calculate the Fc required to keep a 1000 kg car moving at 10 m/s on a curved road with a radius of 30 m. (show all your work)

4. What would happen if the friction between the road and the car tires was less than that size force?

(Fc calculate in #3)

5. Calculate the size of the force required for the same car to go around the same curve at 15 m/s.

6. What happens to the size of the Fc needed to keep the car moving in a curve as the car goes faster? What happens to the size of the force of friction as the car goes faster?

7. Why is it important to pay attention to signs like these posted before curved roadways?

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