LEARNING TARGET JOURNAL
 What is a radian?
 What is the radius of the unit circle?
 What is the circumference of the unit circle?
 How many degrees are in a circle?
 So _____ radians is equivalent to _____ degrees.

NOTES
 Translational motion occurs between one point and another.
 Rotational motion is when a rigid object maintains its shape while rotating around a fixed axis.
 Circular motion is a type of rotational motion that occurs for any object following part of, or an entire circular path.
 The units for measuring angles in radians. (rad)
 Although, many times the measures are left unitless as radian is often an understood angle measure.
 Recall that from the unit circle.
 To convert revolutions to radians, multiply the revolutions by .
 Angular motion is a vector quantity that account for the direction rotation.
 clockwise – which we will account for as negative in direction
 counterclockwise – which we will account for as positive in direction

EXAMPLE 1 – Perform the following conversions.
 125° to radians

 17 radians to degrees

 6800 RPM to rad/s

HOMEWORK 
Physics  Chapter 7  Lesson 29: Angular Kinematics  Notes 
LEARNING TARGET JOURNAL
 What is the difference between angular speed and linear speed?
 What are some similarities of angular motion and linear motion?
 List the any factors you can think of that help angular speed generate faster linear speeds?
 How can it be said that something is said to be traveling at 120 mph when it is not moving in front of us?

NOTES
 Angular displacement () is the change in position as an object rotates.
 s is the arc length
 r is the length of the radius of the circle
 The SI unit for angular displacement is radians. (rad)
 Angular velocity () it is the rate of change in angular displacement.
 The SI base unit for angular velocity is .
 Another common unit for angular velocity is revolutions per minute. (RPM)
 Angular acceleration () is the rate of change in angular velocity.
 The SI base unit for angular acceleration is .
 All these quantities fit the same relationships as their translational counterparts from Chapters 2 & 3.

EXAMPLE 1 – Find the indicated value.
 While riding on a carousel that is rotating clockwise, a child travels through an arc length of 11.5 m. If the child’s angular displacement is 165°, what is the radius of the carousel?

 A car tire rotates with an average angular speed of 29 rad/s. In what time interval will the tire rotate 3.5 times?

 A figure skater begins spinning counterclockwise at an angular speed of 4.0π rad/s. During a 3.0 s interval, she slowly pulls her arms inward and finally spins at 8.0π rad/s. What is her average angular acceleration during this time interval?

EXAMPLE 2 – Use the angular kinematic equations to solve the following.
 Find the angular acceleration of a spinning amusementpark ride that initially travels at 0.50 rad/s then accelerates to 0.60 rad/s during a 0.50 s time interval.

 The wheel on an upsidedown bicycle moves through 11.0 rad in 2.0 s. What is the wheel’s angular acceleration if its initial angular speed is 2.0 rad/s?

 A remotecontrolled car’s wheel accelerates at 22.4 rad/s2 begins with an angular speed of 10.8 rad/s, what is the wheel’s angular speed after exactly three full turns?

HOMEWORK 
Physics  Chapter 7  Lesson 30: Tangential Velocity and Acceleration  Notes 
LEARNING TARGET JOURNAL
 What happens to the rotational speed at the end of a lever when it is shortened?
 TRUE or FALSE: Every point on a wheel travels with the same angular speed? ◻ TRUE ◻ FALSE
 TRUE or FALSE: Every point on a wheel travels with the same tangential speed? ◻ TRUE ◻ FALSE

NOTES
EXAMPLE 1 – Solve the following.
 Find the tangential speed of a ball swung at a constant angular speed of 5.0 rad/s on a rope that is 5.0 m long.

 A woman passes through a revolving door with a tangential speed of 1.8 m/s. If she is 0.80 m from the center of the door, what is the door’s angular speed?

EXAMPLE 2 – Solve the following.
 Find the tangential acceleration of a person standing 9.5 m from the center of a spinning amusementpark ride that has an angular acceleration of 0.15 rad/s2.

 A dog on a merrygoround undergoes a 1.5 m/s2 linear acceleration. If the merrygoround’s angular acceleration is 1.0 rad/s2 dog, how far from the axis of rotation is the dog?

EXAMPLE 3 – A point on the rim of a 0.40 m radius rotating disc has a tangential speed of 4.0 m/s. What is the tangential speed of a point 0.30 m from the center of the same disc?
 First we need to know the angular speed of the disc.

 Since every spot on that disc has the same angular speed, use that value to find the tangential speed at 0.30 m.

HOMEWORK 
Physics  Chapter 7  Lesson 31: Centripetal Acceleration  Notes 
LEARNING TARGET JOURNAL
NOTES
 Centrifugal characterizes the motion of a rotating particle that is “fleeing” the center of rotation.
 Centripetal characterizes the motion of a rotating particle that is “seeking” the center of rotation.
 Centripetal acceleration is the rate of change of the tangential velocity.
 The formula for centripetal acceleration can be used in two forms.
 The variable for centripetal acceleration is .
 The SI unit for centripetal acceleration is .
 The total acceleration of the object is the sum of the tangential acceleration and centripetal acceleration acting at any moment along the circular path.
 It is not a linear sum but a two dimensional sum, because centripetal acceleration acts along the radius of rotation and tangential acceleration acts perpendicular to that radius.

EXAMPLE 1 – Solve the following.
 A 1.2 kg stone is attached to a 1.3 m line and swung in a circle. If the stone has a linear speed of 13 m/s, what is the centripetal acceleration?

 A piece of clay sits 0.20 m from the center of a potter’s wheel. If the potter spins the wheel at an angular speed of 20.5 rad/s, what is the magnitude of the centripetal acceleration of the piece of clay on the wheel?

EXAMPLE 2 – Solve the following.
 A young boy swings a yoyo horizontally above his head so that the yoyo has a centripetal acceleration of 250 m/s2. If the yoyo’s string is 0.50 m long, what is the yoyo’s tangential speed?

 A race car moves along a circular track at an angular speed of 0.512 rad/s. If the car’s centripetal acceleration is 15.4 m/s2 between the car and the center of the track, what is the distance between the car and the center of the track?

HOMEWORK 
Physics  Chapter 7  Lesson 32: Centripetal Force  Notes 
LEARNING TARGET JOURNAL
NOTES
EXAMPLE 1 – Solve the following.
 A 90.0 kg person rides a spinning amusement park ride that has an angular speed of 1.15 rad/s. If the radius of the ride is 11.5 m, what is the magnitude of the force that maintains the circular motion of the person.

 A pilot is flying a small plane at 30.0 m/s in a circular path with a radius of 100.0 m. If a force of 635 N is needed to maintain the pilot’s circular motion, what is the pilot’s mass?

HOMEWORK 
Physics  Chapter 7  Lesson 33: Centripetal Force From Friction  Notes 
LEARNING TARGET JOURNAL
 What are the three types of circular acceleration?
 Describe how each affects the motion of an object traveling in uniform circular motion.

NOTES
EXAMPLE 1 – Solve.
 A 13,500 N car traveling at 50.0 km/h rounds a curve of radius 2.00 × 102 m. Find the minimum coefficient of static friction between the tires and the road that will allow the car to round the curve safely.

 A 2.00 × 103 kg car rounds a circular turn of radius 20.0 m. If the road is flat and the coefficient of static friction between the tires and the road is 0.70, how fast can the car go without skidding?

HOMEWORK 
Physics  Chapter 7  Lesson 34: Newton’s Universal Law of Gravitation  Notes 
LEARNING TARGET JOURNAL
NOTES
 directly proportional to the product of their masses, and
 inversely proportional to the square of the separation between them
 This separation, r, is measured from their centers of mass
 The m here stands for mass of each object
 And G is called the constant of universal gravitation
 The force on each object is the same magnitude, but always attractive so as to follow Newton’s 3rd Law of Motion.

EXAMPLE 1 – Solve the following.
 A 90.0 kg person stands 1.00 m from a 60.0 kg person sitting on a bench nearby. What is the magnitude of the gravitational force between them?

 Mars has a mass of about 6.4 × 1023 kg, and its moon Phobos has a mass of about 9.6 × 1015 kg. If the magnitude of the gravitational force between the two bodies is 4.6 × 1015 N, how far apart are Mars and Phobos?

EXAMPLE 2 – Without using actual mass and separation values, determine how a change in value(s) will affect the gravitational force between two objects.
 If both masses are tripled, what happens to the force?

 If the masses are not changed, but the distance of separation is tripled, what happens to the force?

 If one of the masses is doubled, the other remains unchanged, and the distance of separation is quadrupled, show what happens to the force.

HOMEWORK 
Physics  Chapter 7  Lesson 35: Orbital Velocity  Notes 
LEARNING TARGET JOURNAL
 What is the orbital velocity of a low level satellite?
 What is the orbital velocity of the high level satellites?
 Why do they differ?

NOTES
 Newton’s Universal Law of Gravitation now explains that the attracting force of gravity is the centripetal force
 The most common use for this equation is to find the orbiting speed of a satellite at any given height above the Earth.
Leave space for proof.
 The remaining mass is the mass of the Earth.
 Keep in mind, the orbiting radius is measured from the center of the Earth.
 The radius of the Earth is .

EXAMPLE 1 – Solve the following.
 A satellite has a mass of 100 kg and is in a circular orbit of 2.00 x 106 m above the surface of the Earth. Determine the instantaneous velocity of the satellite in its orbit.

 A satellite moves in a circular orbit around the Earth at a speed of 5000 m/s. Determine the satellite’s altitude above the surface of the Earth.

HOMEWORK 