Physics Chapter on Rolling Motion
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Questions and Answers

What is the expression for total angular momentum when considering rolling motion?

  • $L = ΣI + Σr_i m_i^2 v_i$
  • $L = ΣI + Σr_i m_i v_i$ (correct)
  • $L = ΣI + Σm_iv_i$
  • $L = ΣI + Σr_i^2 m_i v_i$

    • Under which condition does a body exhibit pure rolling motion?

  • When the body is sliding down the incline
  • When the velocity of the contact point is zero (correct)
  • When the velocity of the contact point exceeds the body velocity
  • When there is no friction acting on the body

    • What is the minimum coefficient of friction required for a body to roll down an incline without slipping?

  • $ an heta$
  • $ rac{g heta}{1}$
  • $ rac{1}{g heta}$
  • $ rac{1}{ an heta}$ (correct)

    • What happens when the coefficient of friction is less than the minimum required for pure rolling?

    <p>The body slips downwards with translational acceleration only</p> Signup and view all the answers

    Which expression correctly represents the acceleration of a body rolling down an incline when friction is present and sufficient?

    <p>$a = rac{g an heta}{1 + rac{I}{mR^2}}$</p> Signup and view all the answers

    What is the primary factor that influences the momentum of an object?

    <p>Mass of the object</p> Signup and view all the answers

    Which of the following correctly represents the formula for kinetic energy?

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

    Which principle states that the total mechanical energy in a closed system remains constant?

    <p>Conservation of energy</p> Signup and view all the answers

    In a perfectly elastic collision, which of the following is conserved?

    <p>Both momentum and kinetic energy</p> Signup and view all the answers

    What is the unit of measurement for power in the International System of Units (SI)?

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

    When an object is in free fall, ignoring air resistance, which of the following changes over time?

    <p>Velocity of the object</p> Signup and view all the answers

    Which of the following is true about gravitational potential energy?

    <p>It is directly proportional to height and mass.</p> Signup and view all the answers

    In the context of waves, which property determines the pitch of a sound?

    <p>Frequency of the wave</p> Signup and view all the answers

    What type of energy is stored in objects due to their position or state?

    <p>Potential energy</p> Signup and view all the answers

    Which of the following best describes the relationship between work and energy?

    <p>Work transfers energy.</p> Signup and view all the answers

    What is the correct formula for the $x_{cm}$ of a semicircular ring?

    <p>$x_{cm} = 0$</p> Signup and view all the answers

    When differentiating the position of the center of mass with respect to time, which quantity represents its velocity?

    <p>The derivative of the center of mass coordinates</p> Signup and view all the answers

    According to Newton's second law, which relationship is correctly applied to the center of mass?

    <p>$F = ma_{cm}$</p> Signup and view all the answers

    What principle states that the total momentum of a closed system remains constant?

    <p>Conservation of linear momentum</p> Signup and view all the answers

    The direction of the cross product of two vectors can be determined using which method?

    <p>Right-hand rule</p> Signup and view all the answers

    For a rectangular plate, how is the center of mass typically positioned?

    <p>At the geometric center of the plate</p> Signup and view all the answers

    What is required to calculate the magnitude of the cross product of two vectors?

    <p>The angle between the vectors and their lengths</p> Signup and view all the answers

    In a system where two particles collide, which statement about the center of mass velocity is true?

    <p>Velocity of the center of mass is independent of external forces</p> Signup and view all the answers

    What happens to the center of mass of a system when two particles of equal mass collide elastically?

    <p>It remains stationary</p> Signup and view all the answers

    If an external force acts on a system of particles, how does it affect the center of mass?

    <p>The acceleration of the center of mass is proportional to the net external force</p> Signup and view all the answers

    Which of the following best describes a rigid body?

    <p>A body that maintains a constant distance between all particles</p> Signup and view all the answers

    In rotational motion, how does each particle of a rigid body move?

    <p>In a circle around the axis of rotation</p> Signup and view all the answers

    Which equation calculates the centre of mass (CM) of two particles with masses $m_1$ and $m_2$?

    <p>$ ext{CM} = rac{m_1 ext{r}<em>{1} + m_2 ext{r}</em>{2}}{m_1 + m_2}$</p> Signup and view all the answers

    For which case is the centre of mass representation most complex?

    <p>For a continuous distribution of mass in a rigid body</p> Signup and view all the answers

    What does the variable $M$ represent in the centre of mass equations?

    <p>Total mass of the system</p> Signup and view all the answers

    How does precession change the motion of a spinning body?

    <p>The axis of rotation moves around a vertical axis</p> Signup and view all the answers

    Which of the following statements is true regarding translational motion?

    <p>All particles of a body move with the same velocity at any instant</p> Signup and view all the answers

    What is the formula for the $x_{CM}$ position of a rigid body in a continuous mass distribution?

    <p>$x_{CM} = rac{1}{M} imes ext{Integrand of } x ext{ dm}$</p> Signup and view all the answers

    Which option correctly represents the relationship between rotational and translational motion?

    <p>Rotational motion involves movement in circles around an axis</p> Signup and view all the answers

    What is the primary condition for a body to be in rotational equilibrium?

    <p>The net torque acting on the body must be zero.</p> Signup and view all the answers

    Which equation accurately relates linear velocity to angular velocity for a particle at a distance $r$ from the center of rotation?

    <p>$v = r imes rac{d heta}{dt}$</p> Signup and view all the answers

    How is angular momentum defined in relation to linear momentum?

    <p>$ ext{L} = ext{r} imes ext{p}$ where $ ext{p} = m ext{v}$</p> Signup and view all the answers

    Which physical quantity is analogous to mass in rotational motion?

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

    When a body is in translational equilibrium, which of the following must be true?

    <p>The sum of all external forces acting on it is zero.</p> Signup and view all the answers

    Which statement best describes torque in relation to force?

    <p>Torque is the rotational analogue of force and depends on distance and angle.</p> Signup and view all the answers

    What does the principle of moments state about forces acting on a body?

    <p>If the sum of moments about a fixed point is zero, the body is in rotational equilibrium.</p> Signup and view all the answers

    Which of the following correctly states the relationship between the time rate of angular momentum and torque?

    <p>$ rac{dL}{dt} = au$</p> Signup and view all the answers

    What is the formula for the total kinetic energy of a rigid body in rotational motion?

    <p>$KE = rac{1}{2} imes ext{I} imes ext{ω}^2$</p> Signup and view all the answers

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