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Chapter. Rotational Motion. 8. In this chapter you will:. Learn how to describe and measure rotational motion. Learn how torque changes rotational velocity. Define center of mass and the conditions for equilibrium. Chapter. Table of Contents. 8. Chapter 8: Rotational Motion.
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Chapter Rotational Motion 8 In this chapter you will: • Learn how to describe and measure rotational motion. • Learn how torque changes rotational velocity. • Define center of mass and the conditions for equilibrium.
Chapter Table of Contents 8 Chapter 8: Rotational Motion Section 8.1: Describing Rotational Motion Section 8.2: Rotational Dynamics Section 8.3: Equilibrium Assignments: Read Chapter 8. Study Guide 8 due before the Chapter Test. HW 8.A: p.223: 72-77. HW 8.B: p.224: 81,82,84. p.225: 91,97. HW 8.C: Handout
Section Describing Rotational Motion 8.1 In this section you will: • Describe angular displacement. • Calculate angular velocity. • Calculate angular acceleration. • Solve problems involving rotational motion.
Section Describing Rotational Motion 8.1 Length = d Describing Rotational Motion • A fraction of one revolution can be measured in grads, degrees, or radians. • A grad is 1/400 of a revolution. • A degree is 1/360 of a revolution. • The radianis defined as ½ π of a revolution. The abbreviation of radian is ‘rad’. The distance around the circle is 2π • One complete revolution is equal to 2πradians, so 360 degrees = 2 π radians
Section 8.1 Angular Displacement • The Greek letter theta, θ, is used to represent the angle of revolution. • The counterclockwise rotation is designated as positive, while clockwise is negative. • As an object rotates, the change in the angle is calledangular displacement. • For rotation through an angle, θ, a point at a distance, r, from the center moves a distance given byd = r
Section Describing Rotational Motion 8.1 Angular Velocity • Velocity is displacement divided by the time taken to make the displacement. • The angular velocityof an object is angular displacement divided by the time required to make the displacement. • The angular velocity of an object is given by: = t • Here angular velocity is represented by the Greek letter omega, ω. • The angular velocity is equal to the angular displacement divided by the time required to make the rotation. • Angular velocity is measured in rad/s.
Section Describing Rotational Motion 8.1 Angular Velocity • For Earth, ωE = (2πrad)/(24.0 h)(3600 s/h) = 7.27×10─5 rad/s. • In the same way that counterclockwise rotation produces positive angular displacement, it also results in positive angular velocity. • If an object’s angular velocity is ω, then the linear velocity of a point a distance, r, from the axis of rotation is given by v = r ω. • The speed at which an object on Earth’s equator moves as a result of Earth’s rotation is given by v =r ω = (6.38×106 m) (7.27×10─5rad/s) = 464 m/s. • Earth is an example of a rotating, rigid object. Even though different points on Earth rotate different distances in each revolution, all points rotate through the same angle.
Section Describing Rotational Motion 8.1 Angular Acceleration • Angular accelerationis defined as the change in angular velocity divided by the time required to make that change. • The angular acceleration, α, is represented by the following equation: α = t • Angular acceleration is measured in rad/s2. • If the change in angular velocity is positive, then the angular acceleration also is positive. • The linear acceleration of a point at a distance, r, from the axis of an object with angular acceleration, α, is given by a = r α .
Section Describing Rotational Motion 8.1 Angular Acceleration • A summary of linear and angular relationships. p.200: Practice Problems: 1,2. Section Review: 5,7-10. HW 8.A: p.223: 72-77.
Section Section Check 8.1 Question 1 What is the angular velocity of the minute hand of a clock?
Section Section Check 8.1 Answer 1 Answer:B Reason:Angular velocity is equal to the angular displacement divided by the time required to complete one rotation. In one minute, the minute hand of a clock completes one rotation. Therefore, = 2π rad. Therefore,
Section Section Check 8.1 Question 2 When a machine is switched on, the angular velocity of the motor increases by 10 rad/s for the first 10 seconds before it starts rotating with full speed. What is the angular acceleration of the machine in the first 10 seconds? • π rad/s2 • 1 rad/s2 • 100π rad/s2 • 100 rad/s2
Section Section Check 8.1 Answer 2 Answer:B Reason:Angular acceleration is equal to the change in angular velocity divided by the time required to make that change.
Section Section Check 8.1 Question 3 When a fan performing 10 revolutions per second is switched off, it comes to rest after 10 seconds. Calculate the average angular acceleration of the fan after it was switched off. • 1 rad/s2 • 2π rad/s2 • π rad/s2 • 10 rad/s2
Section Section Check 8.1 Answer 3 Answer:B Reason:Angular displacement of any rotating object in one revolution is 2π rad. Since the fan is performing 10 revolution per second, its angular velocity = 2π×10 = 20π rad/s.Angular acceleration is equal to the change in angular velocity divided by the time required to make that change.
