Physics Vertical Circular Motion Concepts

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

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

Flashcards

Period (T)

The time it takes for an object moving in uniform circular motion to complete one full revolution.

Frequency (f)

The number of revolutions an object completes in uniform circular motion per unit of time. It's the reciprocal of the period.

Uniform Circular Motion (UCM)

Motion of an object moving in a circular path at a constant speed. Only the direction of the velocity changes.

Centripetal Acceleration

The acceleration that acts on an object moving in a circular path, always directed towards the center of the circle.

Signup and view all the flashcards

Non-uniform Circular Motion

Circular motion where the object's speed changes as it moves around the circle. It's a combination of tangential and centripetal acceleration.

Signup and view all the flashcards

Tangential Acceleration (𝑎ԦT)

The acceleration responsible for changing the magnitude (speed) of an object moving in a circular path. It's always tangent to the circular path.

Signup and view all the flashcards

Centripetal Force

The force acting on an object moving in a circular path, always directed towards the center of the circle. It's what keeps the object moving in a circular path.

Signup and view all the flashcards

Centrifugal Force

An apparent outward force that is felt by an object moving in a circular path. It's not a real force but a consequence of inertia.

Signup and view all the flashcards

String

A flexible, thin material that can be stretched or tied, often made of fibers.

Signup and view all the flashcards

Tension (T)

The force exerted by a string or a similar object when it is stretched or pulled tight.

Signup and view all the flashcards

Angular Speed

When an object is rotating around a fixed point, the number of rotations it completes in a unit of time.

Signup and view all the flashcards

Linear Speed

The speed of an object moving in a circular path, measured as the distance traveled per unit of time.

Signup and view all the flashcards

Conical Pendulum

A type of pendulum where the bob swings in a circular path rather than a back-and-forth motion.

Signup and view all the flashcards

Convex Overbridge

A curved surface, like the top of a bridge, where the outside is higher than the inside.

Signup and view all the flashcards

Upper Limit on Speed

The maximum speed a vehicle can have at the top of a convex overbridge without losing contact with the road.

Signup and view all the flashcards

Moment of inertia (I)

The tendency of a body to resist changes in its rotational motion. It depends on the mass distribution and the axis of rotation.

Signup and view all the flashcards

Radius of gyration (K)

The distance from the axis of rotation to a point where the entire mass of the body can be concentrated to have the same moment of inertia as the original body.

Signup and view all the flashcards

Surface density (σ)

A measure of a material's mass per unit area.

Signup and view all the flashcards

Axis of rotation of a disc

The axis of rotation that passes through the center of the object and is perpendicular to its plane.

Signup and view all the flashcards

Concentric Ring

A thin ring with a very small width. It can be treated as a circular object with a uniform radius.

Signup and view all the flashcards

Moment of inertia of a disc calculation

The moment of inertia of a disc is calculated by integrating the moment of inertia of all the concentric rings that make up the disc.

Signup and view all the flashcards

Radius of gyration formula

The square root of the moment of inertia divided by the mass. It is a measure of how spread out the mass is from the axis of rotation.

Signup and view all the flashcards

Moment of inertia of a disc formula

The moment of inertia of a disc is calculated based on the formula MR²/2, where M is the mass and R is the radius. This formula simplifies the calculation of the moment of inertia for this specific shape.

Signup and view all the flashcards

What is the radius of gyration?

A quantity that represents how far away from the rotation axis the mass of an object is effectively concentrated.

Signup and view all the flashcards

How is moment of inertia related to radius of gyration?

The moment of inertia of an object is equal to the product of its mass and the square of its radius of gyration.

Signup and view all the flashcards

What is the physical significance of radius of gyration?

It represents the distance from the axis of rotation where all the mass of an object could be concentrated to have the same moment of inertia as the actual object.

Signup and view all the flashcards

What does the value of the radius of gyration tell us?

It helps us understand how the mass is distributed around the axis of rotation.

Signup and view all the flashcards

What does the equation I = MK^2 imply?

The mass of the object effectively acts at a distance 'K' from the axis of rotation.

Signup and view all the flashcards

How is the radius of gyration related to the distribution of mass?

The larger the radius of gyration, the farther the mass is effectively located from the axis of rotation.

Signup and view all the flashcards

Can we calculate the moment of inertia experimentally?

The moment of inertia of an object can be determined experimentally through the use of the radius of gyration.

Signup and view all the flashcards

What is the importance of radius of gyration in practical applications?

It allows us to calculate moment of inertia for objects with irregular shapes where direct integration may be difficult.

Signup and view all the flashcards

Conservation of Angular Momentum

The angular momentum of a body remains constant if the resultant external torque acting on the body is zero.

Signup and view all the flashcards

Moment of Inertia

The tendency of an object to resist changes in its rotational motion. It depends on the object's mass distribution and its distance from the axis of rotation.

Signup and view all the flashcards

Angular Velocity

The rate at which an object's angular position changes over time.

Signup and view all the flashcards

Angular Acceleration

The change in angular velocity over time. It's the rotational equivalent of acceleration.

Signup and view all the flashcards

Torque

A force that causes an object to rotate, calculated by multiplying the force by the perpendicular distance from the axis of rotation.

Signup and view all the flashcards

Example 1: Ballet Dancer

A dancer starts spinning with arms outstretched, then pulls their arms in. This decreases the moment of inertia, increasing their angular velocity and making them spin faster.

Signup and view all the flashcards

Example 2: Diving

A diver on a board stretches out their body to increase moment of inertia, then tucks their body in to reduce it, increasing their angular velocity for more spins.

Signup and view all the flashcards

Example 3: Ice Skater

A spinning ice skater will slow down when they spread their arms and legs, because this increases their moment of inertia and decreases their angular velocity.

Signup and view all the flashcards

Theorem of Parallel Axes

The moment of inertia of an object about any axis is equal to the sum of its moment of inertia about a parallel axis passing through the center of mass and the product of the object's mass and the square of the distance between the two axes.

Signup and view all the flashcards

Theorem of Perpendicular Axes

This theorem establishes a relationship between the moment of inertias of a flat object about three mutually perpendicular and concurrent axes: two lying in the plane of the object and one perpendicular to it.

Signup and view all the flashcards

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.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

Rotational Dynamics One Shot PDF

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser