02. Torque, Angular Momentum
Rotational Motion

149926 A wheel of mass \(20 \mathrm{~kg}\) and radius \(30 \mathrm{~cm}\) is rotating at an angular speed of \(80 \mathrm{rev} / \mathrm{min}\) when the motor is turned off. Neglecting the friction at the axis, calculate the force that must applied tangentially to the wheel to bring it to rest in 5 revolution.

1 \(1.06 \pi \mathrm{N}\)
2 \(2.06 \pi \mathrm{N}\)
3 \(3.06 \pi \mathrm{N}\)
4 \(4.06 \pi \mathrm{N}\)
Rotational Motion

149927 A uniform disc of radius ' \(a\) ' and mass ' \(m\) ' is rotating freely with an angular speed of ' \(\omega\) ' in a horizontal plane about a smooth fixed vertical axis passing through its center. A particle, also of mass ' \(m\) ' is suddenly attached to the rim of the disc and starts to rotate with it. The new angular speed of this system is

1 \(\frac{\omega}{3}\)
2 \(\frac{\omega}{6}\)
3 \(\frac{\omega}{2}\)
4 \(\frac{\omega}{5}\)
Rotational Motion

149928 Assertion (A): Angular speed, linear speed as Kinetic energy change with time but angular momentum remains constant for a planet orbiting the sun.
Reason (R): Angular momentum is constant as no torque acts on the planet.

1 Both \(\mathrm{A}\) and \(\mathrm{R}\) are true and \(\mathrm{R}\) is a correct explanation for \(\mathrm{A}\)
2 Both \(\mathrm{A}\) and \(\mathrm{R}\) are true but \(\mathrm{R}\) is not a correct explanation for \(\mathrm{A}\)
3 \(\mathrm{A}\) is true. \(\mathrm{R}\) is false
4 \(\mathrm{A}\) is false. \(\mathrm{R}\) is true
Rotational Motion

149929 A thin rod of mass ' \(m\) ' and length ' \(2 l\) ' is made to rotate about an axis passing through its centre and perpendicular to it. Its angular velocity changes from 0 to \(\omega\) in time ' \(t\) '. What is the torque acting on the rod?

1 \(\frac{\mathrm{m} l^{2} \omega}{12 \mathrm{t}}\)
2 \(\frac{\mathrm{m} l^{2} \omega}{\mathrm{t}}\)
3 \(\frac{\mathrm{m} l^{2} \omega}{3 \mathrm{t}}\)
4 \(\frac{4 \mathrm{~m} l^{2} \omega}{3 \mathrm{t}}\)
Rotational Motion

149926 A wheel of mass \(20 \mathrm{~kg}\) and radius \(30 \mathrm{~cm}\) is rotating at an angular speed of \(80 \mathrm{rev} / \mathrm{min}\) when the motor is turned off. Neglecting the friction at the axis, calculate the force that must applied tangentially to the wheel to bring it to rest in 5 revolution.

1 \(1.06 \pi \mathrm{N}\)
2 \(2.06 \pi \mathrm{N}\)
3 \(3.06 \pi \mathrm{N}\)
4 \(4.06 \pi \mathrm{N}\)
Rotational Motion

149927 A uniform disc of radius ' \(a\) ' and mass ' \(m\) ' is rotating freely with an angular speed of ' \(\omega\) ' in a horizontal plane about a smooth fixed vertical axis passing through its center. A particle, also of mass ' \(m\) ' is suddenly attached to the rim of the disc and starts to rotate with it. The new angular speed of this system is

1 \(\frac{\omega}{3}\)
2 \(\frac{\omega}{6}\)
3 \(\frac{\omega}{2}\)
4 \(\frac{\omega}{5}\)
Rotational Motion

149928 Assertion (A): Angular speed, linear speed as Kinetic energy change with time but angular momentum remains constant for a planet orbiting the sun.
Reason (R): Angular momentum is constant as no torque acts on the planet.

1 Both \(\mathrm{A}\) and \(\mathrm{R}\) are true and \(\mathrm{R}\) is a correct explanation for \(\mathrm{A}\)
2 Both \(\mathrm{A}\) and \(\mathrm{R}\) are true but \(\mathrm{R}\) is not a correct explanation for \(\mathrm{A}\)
3 \(\mathrm{A}\) is true. \(\mathrm{R}\) is false
4 \(\mathrm{A}\) is false. \(\mathrm{R}\) is true
Rotational Motion

149929 A thin rod of mass ' \(m\) ' and length ' \(2 l\) ' is made to rotate about an axis passing through its centre and perpendicular to it. Its angular velocity changes from 0 to \(\omega\) in time ' \(t\) '. What is the torque acting on the rod?

1 \(\frac{\mathrm{m} l^{2} \omega}{12 \mathrm{t}}\)
2 \(\frac{\mathrm{m} l^{2} \omega}{\mathrm{t}}\)
3 \(\frac{\mathrm{m} l^{2} \omega}{3 \mathrm{t}}\)
4 \(\frac{4 \mathrm{~m} l^{2} \omega}{3 \mathrm{t}}\)
Rotational Motion

149926 A wheel of mass \(20 \mathrm{~kg}\) and radius \(30 \mathrm{~cm}\) is rotating at an angular speed of \(80 \mathrm{rev} / \mathrm{min}\) when the motor is turned off. Neglecting the friction at the axis, calculate the force that must applied tangentially to the wheel to bring it to rest in 5 revolution.

1 \(1.06 \pi \mathrm{N}\)
2 \(2.06 \pi \mathrm{N}\)
3 \(3.06 \pi \mathrm{N}\)
4 \(4.06 \pi \mathrm{N}\)
Rotational Motion

149927 A uniform disc of radius ' \(a\) ' and mass ' \(m\) ' is rotating freely with an angular speed of ' \(\omega\) ' in a horizontal plane about a smooth fixed vertical axis passing through its center. A particle, also of mass ' \(m\) ' is suddenly attached to the rim of the disc and starts to rotate with it. The new angular speed of this system is

1 \(\frac{\omega}{3}\)
2 \(\frac{\omega}{6}\)
3 \(\frac{\omega}{2}\)
4 \(\frac{\omega}{5}\)
Rotational Motion

149928 Assertion (A): Angular speed, linear speed as Kinetic energy change with time but angular momentum remains constant for a planet orbiting the sun.
Reason (R): Angular momentum is constant as no torque acts on the planet.

1 Both \(\mathrm{A}\) and \(\mathrm{R}\) are true and \(\mathrm{R}\) is a correct explanation for \(\mathrm{A}\)
2 Both \(\mathrm{A}\) and \(\mathrm{R}\) are true but \(\mathrm{R}\) is not a correct explanation for \(\mathrm{A}\)
3 \(\mathrm{A}\) is true. \(\mathrm{R}\) is false
4 \(\mathrm{A}\) is false. \(\mathrm{R}\) is true
Rotational Motion

149929 A thin rod of mass ' \(m\) ' and length ' \(2 l\) ' is made to rotate about an axis passing through its centre and perpendicular to it. Its angular velocity changes from 0 to \(\omega\) in time ' \(t\) '. What is the torque acting on the rod?

1 \(\frac{\mathrm{m} l^{2} \omega}{12 \mathrm{t}}\)
2 \(\frac{\mathrm{m} l^{2} \omega}{\mathrm{t}}\)
3 \(\frac{\mathrm{m} l^{2} \omega}{3 \mathrm{t}}\)
4 \(\frac{4 \mathrm{~m} l^{2} \omega}{3 \mathrm{t}}\)
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Rotational Motion

149926 A wheel of mass \(20 \mathrm{~kg}\) and radius \(30 \mathrm{~cm}\) is rotating at an angular speed of \(80 \mathrm{rev} / \mathrm{min}\) when the motor is turned off. Neglecting the friction at the axis, calculate the force that must applied tangentially to the wheel to bring it to rest in 5 revolution.

1 \(1.06 \pi \mathrm{N}\)
2 \(2.06 \pi \mathrm{N}\)
3 \(3.06 \pi \mathrm{N}\)
4 \(4.06 \pi \mathrm{N}\)
Rotational Motion

149927 A uniform disc of radius ' \(a\) ' and mass ' \(m\) ' is rotating freely with an angular speed of ' \(\omega\) ' in a horizontal plane about a smooth fixed vertical axis passing through its center. A particle, also of mass ' \(m\) ' is suddenly attached to the rim of the disc and starts to rotate with it. The new angular speed of this system is

1 \(\frac{\omega}{3}\)
2 \(\frac{\omega}{6}\)
3 \(\frac{\omega}{2}\)
4 \(\frac{\omega}{5}\)
Rotational Motion

149928 Assertion (A): Angular speed, linear speed as Kinetic energy change with time but angular momentum remains constant for a planet orbiting the sun.
Reason (R): Angular momentum is constant as no torque acts on the planet.

1 Both \(\mathrm{A}\) and \(\mathrm{R}\) are true and \(\mathrm{R}\) is a correct explanation for \(\mathrm{A}\)
2 Both \(\mathrm{A}\) and \(\mathrm{R}\) are true but \(\mathrm{R}\) is not a correct explanation for \(\mathrm{A}\)
3 \(\mathrm{A}\) is true. \(\mathrm{R}\) is false
4 \(\mathrm{A}\) is false. \(\mathrm{R}\) is true
Rotational Motion

149929 A thin rod of mass ' \(m\) ' and length ' \(2 l\) ' is made to rotate about an axis passing through its centre and perpendicular to it. Its angular velocity changes from 0 to \(\omega\) in time ' \(t\) '. What is the torque acting on the rod?

1 \(\frac{\mathrm{m} l^{2} \omega}{12 \mathrm{t}}\)
2 \(\frac{\mathrm{m} l^{2} \omega}{\mathrm{t}}\)
3 \(\frac{\mathrm{m} l^{2} \omega}{3 \mathrm{t}}\)
4 \(\frac{4 \mathrm{~m} l^{2} \omega}{3 \mathrm{t}}\)