Physics Chapter on Motion and Gravity

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

Which of the following statements is NOT true about angular acceleration (α) ?

  • Its direction is determined by the right-hand rule. (correct)
  • It is defined as the change in angular velocity divided by the change in time.
  • It is a vector quantity.
  • It is independent of the mass of the object.

Which of the following statements is TRUE about a planet orbiting the Sun?

  • The planet's speed is fastest when closest to the Sun. (correct)
  • The planet moves fastest when furthest from the Sun.
  • Kepler's laws only apply to planets orbiting the Sun, not other celestial bodies.
  • The planet's speed is constant throughout its orbit.

Which of these quantities is NOT analogous to a corresponding linear quantity?

  • Angular velocity (ω) and linear velocity (v)
  • Angular acceleration (α) and linear acceleration (a)
  • Moment of inertia (I) and mass (m) (correct)
  • Torque (τ) and force (F)

Which of these statements is TRUE regarding Newton's Law of Universal Gravitation?

<p>The force of gravity is inversely proportional to the square of the distance between objects. (B)</p> Signup and view all the answers

Which of these is a correct statement about the motion of planets around the Sun?

<p>The motion of planets around the Sun is governed by the gravitational force between the Sun and the planets. (D)</p> Signup and view all the answers

What formula can be used to determine the horizontal displacement in projectile motion?

<p>R = v0x t (A)</p> Signup and view all the answers

In projectile motion, what remains constant throughout the flight?

<p>The horizontal velocity only (A)</p> Signup and view all the answers

If a bullet hits a target 2 cm below the aiming point and is aimed horizontally, which component primarily affects the vertical distance fallen?

<p>Gravity acting on the bullet (B)</p> Signup and view all the answers

What is the time of flight for a bullet aimed horizontally at a target 30 m away, given that it falls 2 cm (0.02 m) due to gravity?

<p>0.14 seconds (A)</p> Signup and view all the answers

What factor does NOT influence the initial horizontal velocity of a projectile?

<p>The time of flight (C)</p> Signup and view all the answers

What does the variable ∆y represent in the kinematics equation?

<p>The vertical displacement (A)</p> Signup and view all the answers

In the equation ∆y = 21 gt², what is the significance of the term 'g'?

<p>It denotes the gravitational acceleration. (D)</p> Signup and view all the answers

If a projectile is thrown upwards, what sign should the displacement (∆y) be assigned?

<p>Positive (+) (C)</p> Signup and view all the answers

Which of the following best defines the range of a projectile?

<p>The maximum horizontal distance traveled (B)</p> Signup and view all the answers

What is the equation used to calculate the time of flight for a projectile dropped from a height?

<p>t = 2∆y / g (A)</p> Signup and view all the answers

If the height from which the projectile is dropped increases, what happens to the time of flight?

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

In the experiment described, what would happen if both tennis balls were snapped off the table at the same instant?

<p>Both balls hit the ground simultaneously. (C)</p> Signup and view all the answers

What is the initial vertical velocity (v0y) of the projectile when dropped from rest?

<p>0 m/s (A)</p> Signup and view all the answers

What is Kepler’s third law primarily concerned with?

<p>The comparison of orbital periods and average radii of different planets (C)</p> Signup and view all the answers

Which planet has the shortest orbital period?

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

According to Kepler's third law, what happens to the orbital period as the radius of the orbit increases?

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

What does the constant K in Kepler's third law represent?

<p>A proportionality constant for the ratio (B)</p> Signup and view all the answers

Which of the following statements about the T²/R³ ratio is true?

<p>It is the same for Earth and Mars. (A)</p> Signup and view all the answers

For which type of orbits is Kepler's third law valid?

<p>Both circular and elliptical orbits (C)</p> Signup and view all the answers

What is the orbital period of Earth in days?

<p>365 days (B)</p> Signup and view all the answers

How does the mass of the planets affect the validity of Kepler's third law?

<p>It is disregarded, making the law independent of mass. (A)</p> Signup and view all the answers

What is the formula for calculating the maximum height reached by a projectile?

<p>$\frac{V_0^2 \sin^2 \theta}{2g}$ (A)</p> Signup and view all the answers

What is the maximum height reached by a ball kicked at an angle of 37 degrees with an initial velocity of 40 m/s?

<p>28.8 m (D)</p> Signup and view all the answers

What is the formula to determine the horizontal range of a projectile?

<p>$\frac{V_0^2 \sin 2\theta}{g}$ (A)</p> Signup and view all the answers

When a projectile is kicked at an angle of 53 degrees with an initial speed of 25 m/s, what component determines its vertical velocity?

<p>$V_0 \sin \theta$ (A)</p> Signup and view all the answers

What is the horizontal range of the ball kicked at an angle of 37 degrees with an initial velocity of 40 m/s?

<p>153.8 m (D)</p> Signup and view all the answers

What is the time of flight of a projectile kicked at an angle of 53 degrees with an initial speed of 25 m/s before hitting a wall 24 m away?

<p>3.0 s (D)</p> Signup and view all the answers

What determines the maximum height reached in projectile motion?

<p>Both the angle and initial velocity (D)</p> Signup and view all the answers

What is the vertical component of the velocity of a ball just as it hits a 24 m wall if kicked at 25 m/s at 53 degrees?

<p>22.5 m/s (C)</p> Signup and view all the answers

If the distance between two objects is doubled, what happens to the gravitational force between them?

<p>The force is quartered. (B)</p> Signup and view all the answers

A satellite in a circular orbit around Earth experiences a constant acceleration due to gravity. What is the direction of this acceleration?

<p>Towards the center of the Earth. (C)</p> Signup and view all the answers

What is the relationship between the angular velocity (ω) and the linear velocity (v) of a point on a rotating object?

<p>v = rω (B)</p> Signup and view all the answers

What is the relationship between the angular acceleration (α) and the linear acceleration (a) of a point on a rotating object?

<p>a = rα (B)</p> Signup and view all the answers

A projectile is launched horizontally from a cliff. Which of the following statements is TRUE about its motion?

<p>Its horizontal velocity is constant. (A)</p> Signup and view all the answers

Two objects, one with a mass of 1 kg and the other with a mass of 2 kg, are released from rest at the same height above the ground. Which object will reach the ground first?

<p>Both objects will reach the ground at the same time. (C)</p> Signup and view all the answers

What is the relationship between the period (T) of an object's orbit and its orbital radius (r) for an object orbiting a planet?

<p>T² is proportional to r³ (B)</p> Signup and view all the answers

A projectile is launched at an angle of 45 degrees to the horizontal. At what point in its trajectory does the projectile have the greatest vertical velocity?

<p>At the launch point. (A)</p> Signup and view all the answers

Flashcards

Projectile Motion

The motion of an object thrown into the air, affected by gravity.

Time of Flight (t)

The duration an object remains in motion before landing.

Horizontal Displacement (∆x)

The distance traveled in the horizontal direction during motion.

Initial Horizontal Velocity (v0x)

The velocity of an object in the horizontal direction when it starts its motion.

Signup and view all the flashcards

Gravity (g)

The force that attracts objects towards the earth, approximately 10 m/s².

Signup and view all the flashcards

Vertical Displacement (∆y)

The distance an object moves in a vertical direction, influenced by gravity.

Signup and view all the flashcards

Time of Flight

The total time a projectile remains in the air before hitting the ground.

Signup and view all the flashcards

Equation for Vertical Displacement

The formula ∆y = ½ gt² provides vertical displacement for free-falling objects.

Signup and view all the flashcards

Initial Vertical Velocity (v0y)

The starting speed of an object in the vertical direction before any influence of gravity.

Signup and view all the flashcards

Projectile Range

The maximum horizontal distance a projectile travels before hitting the ground.

Signup and view all the flashcards

Sign Convention

The rule that upward motion is positive (+) and downward motion is negative (-) in equations.

Signup and view all the flashcards

Kinematics Equation

A mathematical relation that describes the motion of objects, incorporating displacement, velocity, acceleration, and time.

Signup and view all the flashcards

Maximum Height (H)

The highest vertical position reached by a projectile.

Signup and view all the flashcards

Horizontal Range (R)

The total horizontal distance a projectile travels.

Signup and view all the flashcards

Initial Velocity (V0)

The speed at which a projectile is thrown or kicked.

Signup and view all the flashcards

Angle of Projection (θ)

The angle at which a projectile is launched.

Signup and view all the flashcards

Gravitational Acceleration (g)

The acceleration experienced by objects due to gravity, typically 9.81 m/s².

Signup and view all the flashcards

Vertical Component of Velocity

The component of a projectile's velocity acting upwards or downwards.

Signup and view all the flashcards

Horizontal Component of Velocity

The component of a projectile's velocity acting horizontally.

Signup and view all the flashcards

Resultant Velocity

The overall velocity of a projectile at a given moment.

Signup and view all the flashcards

Kepler’s Third Law

Describes the relationship between the orbital period and radius of planets’ orbits.

Signup and view all the flashcards

Orbital Period (T)

The time taken for a planet to complete one revolution around the Sun.

Signup and view all the flashcards

Average Radius of Orbit (R)

The average distance from the Sun to a planet throughout its orbit.

Signup and view all the flashcards

Proportionality Constant (K)

A constant that relates the orbital period and radius for all planets in Kepler’s third law.

Signup and view all the flashcards

T²/R³ Ratio

The ratio of the square of the orbital period to the cube of the average radius, constant for all planets.

Signup and view all the flashcards

Mercury’s Orbital Period

Mercury takes 88 days to orbit the Sun, the shortest among planets.

Signup and view all the flashcards

Earth’s Orbital Period

Earth takes 365 days to complete its revolution around the Sun.

Signup and view all the flashcards

Saturn’s Orbital Period

Saturn takes 10,759 days to orbit the Sun, the longest among the given planets.

Signup and view all the flashcards

Right-Hand Rule (RHR)

Method to determine the direction of angular velocity (ω) by using your right hand.

Signup and view all the flashcards

Angular Acceleration (α)

The rate of change of angular velocity (ω) over time, defined as α = ∆ω / ∆t.

Signup and view all the flashcards

Torque

The rotational effect of a force applied at a distance from the pivot point.

Signup and view all the flashcards

Moment of Inertia

A measure of an object's resistance to changes in its rotational motion.

Signup and view all the flashcards

Newton's Law of Universal Gravitation

Every object attracts every other object with a force proportional to their masses and inversely to the distance squared.

Signup and view all the flashcards

Gravitational Force

The attraction between two masses, affects their motion.

Signup and view all the flashcards

Acceleration Due to Gravity (g)

The rate of acceleration that objects experience due to Earth's gravity, approximately 9.81 m/s².

Signup and view all the flashcards

Projectile

An object in flight under the influence of gravity after being thrown or projected.

Signup and view all the flashcards

Vertical Motion

The motion of a projectile influenced by gravitational pull, causing constant acceleration.

Signup and view all the flashcards

Angular Motion

The motion of a body rotating around a fixed axis, described by angular position, speed, and acceleration.

Signup and view all the flashcards

Translational Motion

The linear movement of an object from one position to another.

Signup and view all the flashcards

Relationship between Linear and Angular Motion

How linear displacement, speed, and acceleration relate to rotational motion using radius.

Signup and view all the flashcards

Study Notes

Two-Dimensional Motion

  • Kinematics studies motion without considering causes
  • Two-dimensional kinematics extends one-dimensional kinematics (studied in Grade 11)
  • Many natural motions follow curved paths, not straight lines
  • Examples include a ball kicked by a football player, orbital motion of planets, a bicycle rounding a curve, or the rotation of wheels on a car.

Projectile Motion

  • A projectile is an object thrown, fired, or released that moves only under the influence of gravity.
  • Assumptions for projectile motion analysis:
    • Constant free-fall acceleration (g = 9.8 m/s²) always directed downwards
    • Air resistance is negligible
    • Horizontal velocity is constant (no horizontal acceleration)
  • The path of a projectile is a parabola.
  • Horizontal and vertical components are independent

Time of Flight

  • Time of flight is the time taken by the projectile to hit the ground.
  • It can be calculated using the vertical displacement (Δy) and acceleration due to gravity (g)

Range

  • Range is the maximum horizontal distance traveled by the projectile
  • Calculated using the time of flight and horizontal velocity (vox).

Maximum Height

  • Maximum height is the vertical distance reached by a projectile before it starts descending.
  • It can be calculated using the initial vertical velocity (voy), acceleration due to gravity (g), and time of flight.

Inclined Projectile Motion

  • The initial velocity (vo) has both horizontal (vox) and vertical components (voy)
  • Horizontal motion is constant
  • Vertical motion is affected by gravity
  • The path of motion is a parabola
  • The vertical component of velocity is zero at the highest point

Rotational Motion

  • Rotational motion describes the motion of an object revolving around a fixed axis.
  • Examples include the rotation of Earth, a ceiling fan, or a car's wheels.
  • Angular displacement (Δθ) measures the angle through which an object rotates.
  • Angular velocity (ω) is the rate of change of angular displacement (Δθ / Δt).
  • Angular acceleration (α) is rate of change of angular velocity (Δω / Δt).

Relationship Between Linear and Angular Motion

  • There is a direct relationship between linear and angular quantities
  • Linear displacement (s) = radius (r) x angular displacement (Δθ)
  • Linear velocity (v) = radius (r) x angular velocity (ω)
  • Linear acceleration (a) = radius (r) x angular acceleration (α)

Rotational Dynamics

  • Torque (τ) is the rotational effect of a force; τ = rF sin θ
  • Moment of inertia (I) is the resistance of an object to changes in its rotation.
  • Torque and angular acceleration (α) are related through the equation τ = I α

Planetary Motion and Kepler's Laws

  • Planets orbit the Sun in elliptical paths with the Sun at one focus
  • Kepler's first law: The planets orbit the sun in elliptical paths
  • Kepler's second law: A line joining a planet and the Sun sweeps out equal areas during equal intervals of time
  • Kepler's third law: The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit

Newton's Law of Universal Gravitation

  • Every object in the universe attracts every other object with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers (Fg = Gm₁m₂/r²).

Studying That Suits You

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

Quiz Team

Related Documents

Grade 12 Physics Past Paper - Two-Dimensional Motion

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser