A flywheel is revolving with a constant angular velocity. a chip of its rim breaks and flies away. what will be the effect on its angular velocity?

1 Introduction: The Nature of Science and Physics • Introduction to Science and the Realm of Physics, Physical Quantities, and Units • 1.1 Physics: An Introduction • 1.2 Physical Quantities and Units • 1.3 Accuracy, Precision, and Significant Figures • 1.4 Approximation • Glossary • Section Summary • Conceptual Questions • Problems & Exercises • 2 Kinematics • Introduction to One-Dimensional Kinematics • 2.1 Displacement • 2.2 Vectors, Scalars, and Coordinate Systems • 2.3 Time, Velocity, and Speed • 2.4 Acceleration • 2.5 Motion Equations for Constant Acceleration in One Dimension • 2.6 Problem-Solving Basics for One-Dimensional Kinematics • 2.7 Falling Objects • 2.8 Graphical Analysis of One-Dimensional Motion • Glossary • Section Summary • Conceptual Questions • Problems & Exercises • 3 Two-Dimensional Kinematics • Introduction to Two-Dimensional Kinematics • 3.1 Kinematics in Two Dimensions: An Introduction • 3.2 Vector Addition and Subtraction: Graphical Methods • 3.3 Vector Addition and Subtraction: Analytical Methods • 3.4 Projectile Motion • 3.5 Addition of Velocities • Glossary • Section Summary • Conceptual Questions • Problems & Exercises • 4 Dynamics: Force and Newton's Laws of Motion • Introduction to Dynamics: Newton’s Laws of Motion • 4.1 Development of Force Concept • 4.2 Newton’s First Law of Motion: Inertia • 4.3 Newton’s Second Law of Motion: Concept of a System • 4.4 Newton’s Third Law of Motion: Symmetry in Forces • 4.5 Normal, Tension, and Other Examp...

10 Fixed-Axis Rotation • Introduction • 10.1 Rotational Variables • 10.2 Rotation with Constant Angular Acceleration • 10.3 Relating Angular and Translational Quantities • 10.4 Moment of Inertia and Rotational Kinetic Energy • 10.5 Calculating Moments of Inertia • 10.6 Torque • 10.7 Newton’s Second Law for Rotation • 10.8 Work and Power for Rotational Motion • 13 Gravitation • Introduction • 13.1 Newton's Law of Universal Gravitation • 13.2 Gravitation Near Earth's Surface • 13.3 Gravitational Potential Energy and Total Energy • 13.4 Satellite Orbits and Energy • 13.5 Kepler's Laws of Planetary Motion • 13.6 Tidal Forces • 13.7 Einstein's Theory of Gravity • Learning Objectives By the end of this section, you will be able to: • Derive the kinematic equations for rotational motion with constant angular acceleration • Select from the kinematic equations for rotational motion with constant angular acceleration the appropriate equations to solve for unknowns in the analysis of systems undergoing fixed-axis rotation • Use solutions found with the kinematic equations to verify the graphical analysis of fixed-axis rotation with constant angular acceleration In the preceding section, we defined the rotational variables of angular displacement, angular velocity, and angular acceleration. In this section, we work with these definitions to derive relationships among these variables and use these relationships to analyze rotational motion for a rigid body about a fixed axis under a co...

1. A flywheel is revolving with a constant angular velocity. A chip of its rim breaks and flies away. What will be the effect on its angular velocity? 2. The moment of inertia of a uniform circular disc about a tangent in its own plane is 5/4 M MR 2 where M is the mass and R is the radius of the disc. Find its moment of inertia about an axis through its centre and perpendicular to its plane. 3. Derive an expression for maximum safety speed with which a vehicle shouid move along a curved horizontal road. State the significance of it 1. A flywheel is revolving with a constant angular velocity. A chip of its rim breaks and flies away. What will be the effect on its angular velocity? 2. The moment of inertia of a uniform circular disc about a tangent in its own plane is 5/4 M MR 2 where M is the mass and R is the radius of the disc. Find its moment of inertia about an axis through its centre and perpendicular to its plane. 3. Derive an expression for maximum safety speed with which a vehicle shouid move along a curved horizontal road. State the significance of it Updated On Feb 25, 2023 Topic Modern Physics Subject Physics Class Class 12 Answer Type Video solution: 3 Upvotes 197 Avg. Video Duration 8 min

Learning Objectives By the end of this section, you will be able to: • Derive the kinematic equations for rotational motion with constant angular acceleration • Select from the kinematic equations for rotational motion with constant angular acceleration the appropriate equations to solve for unknowns in the analysis of systems undergoing fixed-axis rotation • Use solutions found with the kinematic equations to verify the graphical analysis of fixed-axis rotation with constant angular acceleration In the preceding section, we defined the rotational variables of angular displacement, angular velocity, and angular acceleration. In this section, we work with these definitions to derive relationships among these variables and use these relationships to analyze rotational motion for a rigid body about a fixed axis under a constant angular acceleration. This analysis forms the basis for rotational kinematics. If the angular acceleration is constant, the equations of rotational kinematics simplify, similar to the equations of linear kinematics discussed in Kinematics of Rotational Motion Using our intuition, we can begin to see how the rotational quantities [latex]\theta ,[/latex] [latex]\omega ,[/latex] [latex]\alpha[/latex], and t are related to one another. For example, we saw in the preceding section that if a flywheel has an angular acceleration in the same direction as its angular velocity vector, its angular velocity increases with time and its angular displacement also inc...

Teacher Support The learning objectives in this section will help your students master the following standards: • (4) Science concepts. The student knows and applies the laws governing motion in a variety of situations. The student is expected to: • (C) analyze and describe accelerated motion in two dimensions using equations, including projectile and circular examples. • (D) calculate the effect of forces on objects, including the law of inertia, the relationship between force and acceleration, and the nature of force pairs between objects. In addition, the High School Physics Laboratory Manual addresses content in this section in the lab titled: Circular and Rotational Motion, as well as the following standards: • (4) Science concepts. The student knows and applies the laws governing motion in a variety of situations. The student is expected to: • (D) calculate the effect of forces on objects, including the law of inertia, the relationship between force and acceleration, and the nature of force pairs between objects. Section Key Terms Students may get confused between deceleration and increasing acceleration in the negative direction. In the section on uniform circular motion, we discussed motion in a circle at constant speed and, therefore, constant angular velocity. However, there are times when angular velocity is not constant—rotational motion can speed up, slow down, or reverse directions. Angular velocity is not constant when a spinning skater pulls in her arms, wh...

Learning Objectives By the end of this section, you will be able to: • Use the work-energy theorem to analyze rotation to find the work done on a system when it is rotated about a fixed axis for a finite angular displacement • Solve for the angular velocity of a rotating rigid body using the work-energy theorem • Find the power delivered to a rotating rigid body given the applied torque and angular velocity • Summarize the rotational variables and equations and relate them to their translational counterparts Thus far in the chapter, we have extensively addressed kinematics and dynamics for rotating rigid bodies around a fixed axis. In this final section, we define work and power within the context of rotation about a fixed axis, which has applications to both physics and engineering. The discussion of work and power makes our treatment of rotational motion almost complete, with the exception of rolling motion and angular momentum, which are discussed in Work for Rotational Motion Now that we have determined how to calculate kinetic energy for rotating rigid bodies, we can proceed with a discussion of the work done on a rigid body rotating about a fixed axis. A to B while under the influence of a force [latex]\mathbf.[/latex] [latex]d\mathbf[/latex] is fixed on the rigid body from the origin O to point P. Using the definition of work, we obtain [latex]W=\int \sum \mathbf[/latex], we arrive at the expression for the rotational work done on a rigid body: [latex]dW=(\sum _[/la...

• When the chip of the rim of a flywheel revolving with a constant angular velocity breaks away, its mass will decrease. • Due to the decrease in its mass, the moment of inertia of the flywheel will decrease. • In order to conserve angular momentum, the angular velocity of the flywheel will increase.

Teacher Support The learning objectives in this section will help your students master the following standards: • (4) Science concepts. The student knows and applies the laws governing motion in a variety of situations. The student is expected to: • (C) analyze and describe accelerated motion in two dimensions using equations, including projectile and circular examples. Section Key Terms angle of rotation angular velocity arc length circular motion radius of curvature rotational motion spin tangential velocity Angle of Rotation What exactly do we mean by circular motion or rotation? Rotational motion is the circular motion of an object about an axis of rotation. We will discuss specifically circular motion and spin. Circular motion is when an object moves in a circular path. Examples of circular motion include a race car speeding around a circular curve, a toy attached to a string swinging in a circle around your head, or the circular loop-the-loop on a roller coaster. Spin is rotation about an axis that goes through the center of mass of the object, such as Earth rotating on its axis, a wheel turning on its axle, the spin of a tornado on its path of destruction, or a figure skater spinning during a performance at the Olympics. Sometimes, objects will be spinning while in circular motion, like the Earth spinning on its axis while revolving around the Sun, but we will focus on these two motions separately. Teacher Support [BL] [OL] Explain the difference between circular an...

• When the chip of the rim of a flywheel revolving with a constant angular velocity breaks away, its mass will decrease. • Due to the decrease in its mass, the moment of inertia of the flywheel will decrease. • In order to conserve angular momentum, the angular velocity of the flywheel will increase.

Learning Objectives By the end of this section, you will be able to: • Use the work-energy theorem to analyze rotation to find the work done on a system when it is rotated about a fixed axis for a finite angular displacement • Solve for the angular velocity of a rotating rigid body using the work-energy theorem • Find the power delivered to a rotating rigid body given the applied torque and angular velocity • Summarize the rotational variables and equations and relate them to their translational counterparts Thus far in the chapter, we have extensively addressed kinematics and dynamics for rotating rigid bodies around a fixed axis. In this final section, we define work and power within the context of rotation about a fixed axis, which has applications to both physics and engineering. The discussion of work and power makes our treatment of rotational motion almost complete, with the exception of rolling motion and angular momentum, which are discussed in Work for Rotational Motion Now that we have determined how to calculate kinetic energy for rotating rigid bodies, we can proceed with a discussion of the work done on a rigid body rotating about a fixed axis. A to B while under the influence of a force [latex]\mathbf.[/latex] [latex]d\mathbf[/latex] is fixed on the rigid body from the origin O to point P. Using the definition of work, we obtain [latex]W=\int \sum \mathbf[/latex], we arrive at the expression for the rotational work done on a rigid body: [latex]dW=(\sum _[/la...