Physics Chapter on Rolling Motion

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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?

The body slips downwards with translational acceleration only 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?

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

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

Mass of the object Signup and view all the answers

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

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

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

Conservation of energy Signup and view all the answers

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

Both momentum and kinetic energy Signup and view all the answers

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

Watt Signup and view all the answers

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

Velocity of the object Signup and view all the answers

Which of the following is true about gravitational potential energy?

It is directly proportional to height and mass. Signup and view all the answers

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

Frequency of the wave Signup and view all the answers

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

Potential energy Signup and view all the answers

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

Work transfers energy. Signup and view all the answers

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

$x_{cm} = 0$ Signup and view all the answers

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

The derivative of the center of mass coordinates Signup and view all the answers

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

$F = ma_{cm}$ Signup and view all the answers

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

Conservation of linear momentum Signup and view all the answers

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

Right-hand rule Signup and view all the answers

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

At the geometric center of the plate Signup and view all the answers

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

The angle between the vectors and their lengths Signup and view all the answers

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

Velocity of the center of mass is independent of external forces Signup and view all the answers

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

It remains stationary Signup and view all the answers

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

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

Which of the following best describes a rigid body?

A body that maintains a constant distance between all particles Signup and view all the answers

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

In a circle around the axis of rotation Signup and view all the answers

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

$ ext{CM} = rac{m_1 ext{r}{1} + m_2 ext{r}{2}}{m_1 + m_2}$ Signup and view all the answers

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

For a continuous distribution of mass in a rigid body Signup and view all the answers

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

Total mass of the system Signup and view all the answers

How does precession change the motion of a spinning body?

The axis of rotation moves around a vertical axis Signup and view all the answers

Which of the following statements is true regarding translational motion?

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

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

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

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

Rotational motion involves movement in circles around an axis Signup and view all the answers

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

The net torque acting on the body must be zero. 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?

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

How is angular momentum defined in relation to linear momentum?

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

Which physical quantity is analogous to mass in rotational motion?

Moment of inertia Signup and view all the answers

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

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

Which statement best describes torque in relation to force?

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

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

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

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

$rac{dL}{dt} = au$ Signup and view all the answers

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

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