Physics Vertical Circular Motion Concepts
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Questions and Answers

What force acts vertically upwards at the lowermost position of a bob in vertical circular motion?

  • Weight (mg)
  • Tension (TB) (correct)
  • Normal reaction force
  • Centrifugal force

    • The tension in a string is always necessary for a bob to perform vertical circular motion.

    False (B)

    What force is responsible for changing the direction of velocity in vertical circular motion?

    Tension

    In a sphere of death, the normal reaction force replaces the _________ in vertical circular motion.

    <p>tension</p> Signup and view all the answers

    Match the following concepts with their corresponding definitions:

    <p>Centripetal Force = Changes the direction of motion Tension = Force exerted by a string Normal Reaction Force = Force exerted by a surface Gravitational Force = Weight of an object</p> Signup and view all the answers

    Which component of weight contributes to changing the speed of a bob during vertical motion?

    <p>Tangential component (D)</p> Signup and view all the answers

    In the context of the upper limit speed for a vehicle on a convex bridge, the normal force and weight must combine to provide centripetal force.

    <p>True (A)</p> Signup and view all the answers

    What happens to the speed of a bob while going up in vertical circular motion?

    <p>Decreases</p> Signup and view all the answers

    What happens to the velocity of an object in uniform circular motion?

    <p>Only the direction changes (C)</p> Signup and view all the answers

    Centripetal force acts outwards from the center of the circular path.

    <p>False (B)</p> Signup and view all the answers

    Define centripetal acceleration.

    <p>Centripetal acceleration is the acceleration directed towards the center of the circular path.</p> Signup and view all the answers

    The time taken to complete one revolution in uniform circular motion is called the ______.

    <p>period</p> Signup and view all the answers

    Match the types of circular motion with their characteristics:

    <p>Uniform Circular Motion = Speed is constant but direction changes Non-uniform Circular Motion = Speed is variable and direction changes Centripetal Acceleration = Directed towards center of circular path Tangential Acceleration = Changes the magnitude of velocity</p> Signup and view all the answers

    Which of the following is an example of centrifugal force?

    <p>A rider feeling pushed outward while on a merry-go-round (C)</p> Signup and view all the answers

    Tangential acceleration is always directed toward the center of the circular path.

    <p>False (B)</p> Signup and view all the answers

    What is the frequency of revolution in circular motion?

    <p>The frequency of revolution is the number of revolutions performed by a particle in unit time.</p> Signup and view all the answers

    What is the moment of inertia for a circular disc of mass M and radius R rotating about its own axis?

    <p>$\frac{1}{2} MR^2$ (D)</p> Signup and view all the answers

    The radius of gyration for a circular disc is equal to its radius.

    <p>False (B)</p> Signup and view all the answers

    What does the term 'radius of gyration' refer to in the context of the moment of inertia?

    <p>It refers to the distance from the axis of rotation at which the mass of the body could be concentrated without changing its moment of inertia.</p> Signup and view all the answers

    The moment of inertia of a solid cylinder with mass M and radius R, coinciding with its axis, is ___.

    <p>$\frac{1}{2} MR^2$</p> Signup and view all the answers

    Match the following bodies with their respective moment of inertia about the specified axis:

    <p>Thin uniform rod = $\frac{1}{12} ML^2$ Thin uniform ring = $MR^2$ Circular disc = $\frac{1}{2} MR^2$ Solid cylinder = $\frac{1}{2} MR^2$</p> Signup and view all the answers

    For a thin uniform ring of mass M and radius R, what is the moment of inertia about its central axis?

    <p>$MR^2$ (D)</p> Signup and view all the answers

    A higher radius results in a higher moment of inertia for a uniform disc, all other factors being equal.

    <p>True (A)</p> Signup and view all the answers

    What is the significance of the moment of inertia in physics?

    <p>It quantifies the resistance of a body to angular acceleration about a rotational axis.</p> Signup and view all the answers

    What is the formula that relates moment of inertia (I), mass (M), and radius of gyration (K)?

    <p>I = M*K^2 (C)</p> Signup and view all the answers

    The larger the radius of gyration, the closer the mass is to the axis of rotation.

    <p>False (B)</p> Signup and view all the answers

    What does the radius of gyration represent in relation to mass distribution?

    <p>The radius of gyration represents the effective distance at which the mass of an object can be considered to act from the axis of rotation.</p> Signup and view all the answers

    The moment of inertia of a hollow sphere coinciding with any diameter is expressed as ______.

    <p>MR^2/3</p> Signup and view all the answers

    Match the following shapes with their corresponding moment of inertia formulas:

    <p>Solid Sphere = MR^2/5 Hollow Sphere = MR^2/3 Hollow Cylinder = MR^2/6 Solid Cylinder = MR^2/2</p> Signup and view all the answers

    Which of the following describes the radius of gyration?

    <p>It is the distance from the axis at which the mass acts. (B)</p> Signup and view all the answers

    The moment of inertia can be determined directly for any object regardless of its shape.

    <p>False (B)</p> Signup and view all the answers

    Explain the physical significance of the radius of gyration.

    <p>The radius of gyration provides insight into how an object's mass is distributed relative to its axis of rotation, influencing its resistance to angular acceleration.</p> Signup and view all the answers

    What does the radius of gyration signify?

    <p>Distribution of mass about the axis of rotation (B)</p> Signup and view all the answers

    The theorem of parallel axes states that the moment of inertia about any axis is the sum of the moment of inertia about the center of mass and the product of mass and square of the distance between the axes.

    <p>True (A)</p> Signup and view all the answers

    What is the condition to apply the theorem of parallel axes?

    <p>There must be two parallel axes with one passing through the center of mass.</p> Signup and view all the answers

    The theorem of perpendicular axes applies to objects that are _____ dimensional.

    <p>two</p> Signup and view all the answers

    Match the components related to moment of inertia with their descriptions:

    <p>IC = Moment of inertia about the center of mass IO = Moment of inertia about any axis passing through point O h = Distance between two parallel axes dm = Mass element at a point</p> Signup and view all the answers

    Which of the following objects can be analyzed using the theorem of perpendicular axes?

    <p>A disc (C)</p> Signup and view all the answers

    The radius of gyration is the distance from the center of mass to the axis of rotation.

    <p>False (B)</p> Signup and view all the answers

    State the theorem of perpendicular axes.

    <p>The moment of inertia of a laminar object about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two axes in its plane.</p> Signup and view all the answers

    What happens to a dancer's angular speed when they decrease their moment of inertia by folding their arms?

    <p>It increases (B)</p> Signup and view all the answers

    The statement 'Angular momentum is conserved when an external torque is applied' is true.

    <p>False (B)</p> Signup and view all the answers

    State the principle of conservation of angular momentum.

    <p>The angular momentum of a body remains constant if the resultant external torque acting on the body is zero.</p> Signup and view all the answers

    When divers leave the diving board, they __________ their body to reduce inertia and increase angular speed.

    <p>fold</p> Signup and view all the answers

    Match the following scenarios with their effect according to the conservation of angular momentum:

    <p>Ballet Dancers = Increase in angular speed when arms are folded Diving = Increase in angular speed when body is tucked Stretching arms and legs = Increase in moment of inertia Retracting limbs during a spin = Decrease in moment of inertia</p> Signup and view all the answers

    Which of the following statements is true regarding the moment of inertia and angular speed?

    <p>Decreasing moment of inertia leads to increased angular speed (A)</p> Signup and view all the answers

    A ballet dancer increases their angular speed by spreading their arms wide.

    <p>False (B)</p> Signup and view all the answers

    Describe one example of how divers use angular momentum in a dive.

    <p>Divers tuck their body to decrease moment of inertia and increase angular speed during flips.</p> Signup and view all the answers

    Study Notes

    Rotational Dynamics

    • This subject matter pertains to the study of rotational motion, including concepts like torque, angular momentum, moment of inertia, and related equations, particularly within the context of HSC Board 2025 Physics.

    Uniform Circular Motion (UCM)

    • UCM describes a circular motion where the speed of the object remains constant.
    • The direction of velocity, however, changes continuously. This constant change in direction signifies acceleration.
    • This acceleration is directed towards the center of the circle and is known as centripetal acceleration.
    • The formula for this acceleration is ac = v2/r, where ac is centripetal acceleration, v is the speed, and r is the radius of the circular path.

    Period and Frequency

    • Period (T) is the time taken for one complete revolution.
    • Frequency (n) is the number of revolutions per unit time.
    • The relationship between period and frequency is n = 1/T.
    • The relationship between linear velocity, angular velocity and radius is v = ωr.

    Centripetal Force

    • Centripetal force is the force required to keep an object moving in a circular path.
    • It is always directed towards the center of the circle.
    • The equation is Fc = mac = mv2/r.

    Centrifugal Force

    • Centrifugal force is an apparent outward force that arises in a rotating frame of reference.
    • It is not a real force, but rather a consequence of inertia.
    • The magnitude of centrifugal force is equal to that of centripetal force, with opposite direction.

    Non-uniform Circular Motion

    • In non-uniform circular motion, the speed of the object changes along with its direction.
    • There exist two types of accelerations.
    • Tangential acceleration (at) changes the speed of the object. The equation for this tangential acceleration is at = (Δv)/(Δt), where Δv is a change in velocity and Δt is a change in time (at is directed along the tangent to the circle).
    • Radial or Centripetal acceleration (ac) changes the direction of the object's velocity (ac is directed along the radius). The equation for this centripetal acceleration remains the same (ac = v2/r).

    Applications

    • Vehicles on horizontal circular tracks and banking on curved roads
    • Well of death stunts
    • Conical Pendula
    • Vertical Circular Motion (roller coasters, water in a bucket)

    Moment of Inertia

    • It is a measure of a body's resistance to rotational acceleration. It depends both on the mass of the object and how that mass is distributed relative to the axis of rotation.
    • The equation is I = Σmr2.

    Rolling Motion

    • Rolling motion occurs when a body spins and simultaneously translates.
    • The kinetic energy of a rolling body combines translational and rotational components.
    • The expression for kinetic energy of a rolling body is KE = ½MV2 + ½IW2 (or KE = ½MV2 + ½MK2ω2)where I is moment of inertia and K is the radius of gyration.

    Conservation of Angular Momentum

    • The angular momentum of a system remains constant if there is no net external torque acting on the system.
    • The law is useful in explaining phenomena such as the changing angular velocity of a ballet dancer or a diver during a routine in a swimming pool, as they respectively change their body positioning.

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    Rotational Dynamics One Shot PDF

    Description

    Test your understanding of vertical circular motion with this quiz. Questions cover key forces like tension, normal force, and centripetal force involved in the motion of a bob. Determine how these forces interact and impact the speed and direction of the motion.

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