Question

What is the relations between torque and angular momentum in 11th physics book

Answer 1

Answer:

$\boxed{ \sf{ \red{ \bold{ \large{Torque}}}}}$

• It is defined as the Moment of Force.
• It is an axial vector
• It is an index representing the amount of force required to rotate something around a given axis.

Mathematically :

$\boxed{ \sf{ \large{ \blue{ \vec \tau = \vec r \: \times \: \vec F }}}}$

$\boxed{ \large{ \sf{ \bold{ \red{Angular \: Momentum}}}}}$

• It is the rotational analogue of Linear Momentum.
• It is given by product of Moment of Inertia and Angular Velocity.

$\boxed{ \blue{ \sf{ \large{L \: = I \times \omega}}}}$

$\boxed{ \sf{ \orange{ \huge{ \bold{Relationship}}}}}$

Torque is the rate of change of Angular Momentum with respect to time.

$\: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \sf{ \huge{ \green{ \bold{ \tau = \dfrac{dL}{dt}}}}}}$

Answer 2

$\underline{ \boxed{ \mathfrak{ \huge{ \pink{Answer}}}}} \\ \\ \star \: \underline{ \boxed{ \orange{ \rm{Torque \: ( \vec{ \tau})}}}}$

• Torque acts only in circular motion
• Torque is axial vector quantity
• Torque is the cross product of radius and Force
• Dimentional formula of torque is [M(1)L(2)T(-2)]

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed{ \rm{ \red{ \vec{\tau} = r \times \vec{F}}}}}$

$\star \: \underline{ \boxed{ \orange{ \rm{Angular \: Momentum \: ( \vec{L})}}}}$

• Angular momentum is also axial vector quantity
• Angular momentum is cross product of moment of inertia and angular velocity
• Angular momentum also defined as cross product of radius and Linear momentum
• Dimentional formula of Angular momentum is [M(1)L(2)T(-1)]

$\: \: \: \: \: \: \boxed{ \boxed{ \rm{ \red{ \vec{L} = I \: \times \: \vec{ \omega} = r \: \times \: \vec{P} }}}}$

$\\ \\ \star \: \underline{\boxed{ \rm{ \blue{Relationship\: :- \: {bet}^{n} \: \red{\vec{\tau }}\: and \: \red{\vec{ L} }}}}} \\ \\ \huge{ \dagger} \: \: \boxed{\boxed{ \rm{ \purple{ \huge{ \vec{ \tau} = \frac{d{ \vec{L}}}{dt} }}}} }\: \: \huge{ \dagger}$