A LevelPhysicsEdexcelFlashcards6. Further MechanicsCircular Motion

Circular Motion (Edexcel A Level Physics): Flashcards

Exam code: 9PH0

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  • Define radian.

    The angle subtended at the centre of a circle by an arc equal in length to the radius of the circle

  • Define angular displacement.

    The change in angle, in radians, of a body as it moves in a circle, measured with respect to the centre of orbit

  • What equation relates angular displacement to arc length and radius?

    \Delta \theta = \frac{s}{r}

    where s = arc length (m) and r = radius of the circle (m)

  • Angular displacement describes the change in angle, in .........., of a body as it moves in a circle

    Angular displacement describes the change in angle, in radians, of a body as it moves in a circle

  • How many radians are there in a complete circle?

    2π radians (about 6.28 rad), so π radians = 180°

  • What is 1 radian in degrees?

    1 rad ≈ 57.3°, found from \frac{360°}{2\pi}

  • True or False?

    The equation Δθ = s/r gives the angle in degrees

    False.

    The equation gives the angular displacement in radians. Convert to degrees separately only if the question requires it

  • Define angular velocity.

    The rate of change of angular displacement — the angle swept out per second. It is a vector, measured in rad s-1

  • What equation defines angular velocity ω?

    \omega = \frac{\Delta \theta}{\Delta t}

    where Δθ = change in angular displacement (rad) and Δt = time interval (s)

  • How can angular velocity ω be expressed in terms of linear speed, frequency and time period?

    \omega = \frac{v}{r} = 2\pi f = \frac{2\pi}{T}

    where T = time period (s) and f = frequency (Hz)

  • What equation links linear speed v and angular speed ω?

    v = \omega r

    where r = radius of the orbit (m)

  • Angular velocity is a .......... quantity, whereas angular speed is its ..........

    Angular velocity is a vector quantity, whereas angular speed is its magnitude

  • True or False?

    For two objects with the same linear speed, the one further from the centre of orbit has the greater angular velocity

    False.

    For the same linear speed v, a larger radius r gives a smaller angular velocity, since \omega = \frac{v}{r}

  • Why is ω sometimes called angular frequency?

    Because of its relationship to linear frequency f, given by \omega = 2\pi f. Note ω is measured in rad s-1, whereas f is in Hz

  • Why is an object moving at constant speed in a circle still accelerating?

    Its direction is constantly changing, so its linear velocity changes. A changing velocity means the object is accelerating, directed toward the centre (centripetal)

  • Define centripetal acceleration.

    The acceleration of an object towards the centre of a circle when it moves around the circle at constant speed

  • State the equations for centripetal acceleration in terms of v, r and ω

    a = \frac{v^2}{r} = r\omega^2 = v\omega

    where v = linear speed, ω = angular speed and r = radius

  • What does the negative sign in a = -\frac{v^2}{r} indicate?

    That the centripetal acceleration is directed toward the centre of the orbit

  • In deriving centripetal acceleration, the .......... approximation is used, where sin θ ≈ θ for very small angles in radians

    In deriving centripetal acceleration, the small angle approximation is used, where sin θ ≈ θ for very small angles in radians

  • True or False?

    Centripetal acceleration points in the same direction as the object's velocity

    False.

    Centripetal acceleration is always directed toward the centre of the circle, which is perpendicular to the object's velocity

  • How is the instantaneous centripetal acceleration obtained in the derivation?

    By reducing the angular displacement θ until it is infinitesimally small (taking the limit θ → 0), where \frac{\sin\theta}{\theta} \approx 1

  • Why does an object moving in a circle require a resultant force?

    It is not in equilibrium — it constantly changes direction. A resultant force, the centripetal force, is needed to keep it moving in a circle

  • Define centripetal force.

    The resultant force towards the centre of the circle required to keep a body in uniform circular motion. It is always directed toward the centre of rotation

  • Centripetal force and centripetal acceleration act in the .......... direction, as a consequence of ..........

    Centripetal force and centripetal acceleration act in the same direction, as a consequence of Newton's second law

  • True or False?

    Centripetal force is a separate, distinct type of force

    False.

    Centripetal force is not a separate force — it is the name for whatever resultant force (e.g. tension, gravity, electric or magnetic) happens to point toward the centre

  • Give examples of forces that can provide the centripetal force

    Any force directed toward the centre, such as:

    • tension in a string

    • gravity on an orbiting satellite

    • the electric force on a charge

    • the magnetic force on a moving charged particle

  • State the equations for centripetal force in terms of v, r and ω

    F = \frac{mv^2}{r} = mr\omega^2 = mv\omega

    where m = mass, v = linear speed, ω = angular speed and r = radius

  • In what direction does the centripetal force always act?

    Toward the centre of the circle, perpendicular to the object's direction of travel

  • The centripetal force is the .......... force on an object moving in a circle

    The centripetal force is the resultant force on an object moving in a circle

  • For a ball swung on a string in a vertical circle, where is it fastest and where is the tension greatest?

    Fastest at the bottom (lowest gravitational potential energy) and slowest at the top. The tension is greatest at the bottom and least at the top

  • For vertical circular motion, what is the tension at the bottom of the circle?

    T_{max} = \frac{mv^2}{r} + mg

    The tension must both support the weight and provide the centripetal force

  • For vertical circular motion, what is the tension at the top of the circle?

    T_{min} = \frac{mv^2}{r} - mg

    Here the weight and tension both act toward the centre, so together they provide the centripetal force

  • What is the minimum speed at the top of a vertical circle so the object stays on its path?

    When the tension T = 0, the weight alone provides the centripetal force, so \frac{mv^2}{r} = mg giving v = \sqrt{gr}

  • True or False?

    At the top of a vertical circle, the tension in the string is equal to the centripetal force

    False.

    The centripetal force is the resultant of tension and weight. At the top both act toward the centre, so \frac{mv^2}{r} = T + mg — tension alone is not the centripetal force

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