Rotational Motion for General Physics 1, Grade 12
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Questions and Answers

What is the SI unit for angular momentum?

  • rad/s
  • kg∙m/s
  • kg∙m²/s²
  • kg∙m²/s (correct)

    • How is angular acceleration defined?

  • Change in angular velocity per unit time (correct)
  • Change in angular displacement over time squared
  • Change in angular displacement per unit time
  • Change in torque per unit time

    • What does a negative angular velocity indicate?

  • No rotation
  • Clockwise rotation (correct)
  • Counterclockwise rotation
  • Constant velocity

    • Which of the following describes the relationship between torque and angular momentum?

    <p>Torque is the derivative of angular momentum with respect to time</p> Signup and view all the answers

    During a rotational motion, if a skater pulls their arms closer to their body, what happens to their angular momentum?

    <p>Remains the same</p> Signup and view all the answers

    Which equation represents the rotational analogue of Newton's second law based on angular momentum?

    <p>∑τ = I*α</p> Signup and view all the answers

    What happens to angular velocity during a constant moment of inertia if torque is applied?

    <p>Increases proportionally to the applied torque</p> Signup and view all the answers

    What does angular displacement measure?

    <p>The angle swept out by a line through a rotating body</p> Signup and view all the answers

    What does a larger moment of inertia indicate about the difficulty of rotational motion?

    <p>It requires more force to change the rotational motion.</p> Signup and view all the answers

    How is the moment of inertia calculated for a single particle?

    <p>Mass multiplied by the square of its distance from the axis.</p> Signup and view all the answers

    What happens to the moment of inertia when a mass is moved further from the axis of rotation?

    <p>It increases.</p> Signup and view all the answers

    In which configuration would a body have the greatest moment of inertia?

    <p>When arms and legs are extended perpendicular to the axis.</p> Signup and view all the answers

    Which statement correctly describes the radius of gyration?

    <p>It indicates how mass is concentrated relative to the axis of rotation.</p> Signup and view all the answers

    What does the moment of inertia depend on when calculated for a system of particles?

    <p>The sum of the individual distances and masses of all particles.</p> Signup and view all the answers

    Why is it important to determine the axis of rotation when calculating moment of inertia?

    <p>Because moment of inertia varies with different axes.</p> Signup and view all the answers

    What effect does increasing the distance of a mass from the axis of rotation have on angular momentum?

    <p>It increases angular momentum if the rotational velocity is constant.</p> Signup and view all the answers

    What happens to angular momentum when the net external torque acting on a system is zero?

    <p>Angular momentum remains constant.</p> Signup and view all the answers

    In the case of a spinning figure skater, what is the relationship between moment of inertia and angular speed?

    <p>As moment of inertia decreases, angular speed increases.</p> Signup and view all the answers

    What is the moment of inertia of the skater when her arms are stretched?

    <p>3.0 kg·m²</p> Signup and view all the answers

    How many revolutions per second does the skater make with her arms stretched?

    <p>3 revolutions per second</p> Signup and view all the answers

    When the skater brings her arms close to her body, what happens to her total angular momentum?

    <p>It remains the same as before.</p> Signup and view all the answers

    If the skater’s moment of inertia is 2.2 kg·m² when her arms are close to her chest, what is her new angular speed?

    <p>4 revolutions per second</p> Signup and view all the answers

    Which of the following statements about angular momentum is incorrect?

    <p>Angular momentum is always conserved.</p> Signup and view all the answers

    Why does the skater spin faster when her arms are closer together?

    <p>Moment of inertia decreases.</p> Signup and view all the answers

    Study Notes

    Rotational Motion for General Physics 1/ Grade 12

    • This self-learning kit is designed for STEM students
    • The activities are aligned with the Most Essential Learning Competencies (MELCs)
    • The kit simplifies the concepts for better understanding
    • It covers calculations for moment of inertia, torque, and rotational quantities
    • Students learn to describe rotational quantities using vectors
    • The kit emphasizes determining static equilibrium
    • Rotational kinematic relations for constant angular accelerations are applied
    • Skills in solving static equilibrium problems are enhanced
    • Students become critical problem-solvers, effective communicators, and responsible citizens

    Objectives

    • Students will be able to describe rotational quantities using vectors
    • Students will be able to calculate the moment of inertia about a given axis
    • Students will be able to calculate the magnitude and direction of torque
    • Students will be able to solve static equilibrium problems
    • Students will be able to display appreciation for the application of rotational motion in daily life

    Learning Competencies

    • Calculate the moment of inertia for single and multiple objects
    • Calculate magnitude and direction of torque using vector cross product
    • Describe rotational quantities with vectors
    • Determine whether a system is in static equilibrium
    • Apply rotational kinematic relations for constant angular acceleration
    • Calculate angular momentum for different systems
    • Apply the torque-angular momentum relation
    • Solve static equilibrium problems (e.g., see-saws, cable systems, ladders, scales)

    Pre-Test (Concepts in a Box)

    • Relationships between rotational and linear motion, as expressed in listed concepts (e.g., Kepler's laws, kinematics, linear motion, escape velocity, law of equal areas, angular quantities, planetary motion, law of ellipses) are organized in a chart
    • These concepts include relationships between linear and rotational motion, describing motion in relation to an axis, Newtonian Law of Gravity, and other concepts related to rotational motion

    Modified True or False

    • Torques are associated with rotation
    • Moment Arm is perpendicular distance from a force's line to axis of rotation
    • Applying force creates movement
    • Moment of arm is also leverage
    • Measuring a force to rotate an object around an axis is called torque
    • Positive torque occurs with counter-clockwise and negative with clockwise rotation
    • Measuring rotation caused by a force
    • The pivot point or fulcrum is the rotation point.

    Inertia

    • Inertia is an object's tendency to resist change in its state of motion
    • Inertia applies to objects in rotational motion as well (resisting change in rotation)
    • Moment of Inertia (rotational inertia) measure of the resistance a rotating object has to changing its state of rotation
    • The SI unit for moment of inertia is kg·m²
    • Objects with mass further from the axis of rotation have greater moment of inertia

    Moment of Inertia (Rotational inertia)

    • Objects resist any changes in motion
    • Moment of Inertia depends on mass distribution; mass far from axis has higher inertia
    • Examples provided: dumbbells

    Radius of Gyration (k)

    • Distance from axis where mass is concentrated to keep moment of inertia unchanged
    • Analogous to center of mass

    Moment of Inertia of Uniform and Regular Shaped Bodies

    • Formulas provided for different shapes (solid cylinder, solid sphere, thin ring, etc.)
    • These are used to determine moment of inertia

    Examples

    • Calculating moment of inertia for a solid cylinder
    • Calculating moment of inertia and radius of gyration for a baton

    Torque

    • Torque is force's effectiveness in rotating a body
    • Measured by multiplying the applied force by the perpendicular distance from the axis of rotation
    • Units are meter-newton (m·N)

    Torque Orientation

    • Force direction affects rotation
    • Maximum torque occurs with perpendicular alignment of force and axis of rotation

    Angular Velocities

    • Time rate of angular displacement changes
    • Expressed in deg/s, rad/s, or rev/s

    Angular Acceleration

    • The time rate of change in angular velocity
    • Measured in rad/s² or rev/s²

    Static Equilibrium

    • State of a body at rest, zero acceleration, and zero net force
    • Center of gravity is where body's weight is concentrated
    • Stability depends on center of gravity location relative to base
    • Stable objects have lower centers of gravity and wider base

    Conditions for Equilibrium

    • First condition: Net force is zero
    • Second condition: Net torque is zero
    • The object is in translational and rotational equilibrium when both of these conditions are met

    Equilibrant

    • Force needed to balance the resultant of forces
    • Equal in magnitude to the resultant force but in opposite direction

    Angular Momentum

    • Rotational analogue of linear momentum.
    • Momentum is the product of inertia and angular velocity
    • Units are kg·m²/s
    • Angular momentum of a rotating object remains constant when net torque is zero.

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    Description

    This quiz focuses on rotational motion concepts tailored for Grade 12 STEM students. It covers essential calculations such as moment of inertia, torque, and the application of rotational kinematic relations. Enhance your skills in describing rotational quantities and solving static equilibrium problems.

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