The torque - on a body about a given point is found to be equal to A-L- where A- is a constant vector and L- is the angular momentum of the body about that point- From this it follows that -

The correct options are A dL⃗dt is perpendicular to L⃗ at all instants of time. B the components of the L⃗ in the direction of A⃗ do not ...

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Byju's Answer

Standard XII

Physics

Newton's Second Law: Rotatory Version

The torque ...

Question

The torque $\to τ$ on a body about a given point is found to be equal to $\to A \times \to L$ where $\to A$ is a constant vector and $\to L$ is the angular momentum of the body about that point. From this it follows that :

\frac{d \to L}{d t}

is perpendicular to

\to L

at all instants of time.

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the components of the

\to L

in the direction of

\to A

do not change with time.

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the magnitude of

\to L

does not change with time.

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\to L

does not change with time.

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Solution

The correct options are
A $\frac{d \to L}{d t}$ is perpendicular to $\to L$ at all instants of time.
B the components of the $\to L$ in the direction of $\to A$ do not change with time.
C the magnitude of $\to L$ does not change with time.
As $\to τ = \to A \times \to L$ , so $\to τ$ is perpendicular to $\to L$ .
also $\to τ = \frac{d \to L}{d t}$ . Thus , $\frac{d \to L}{d t}$ is perpendicular to $\to L$ at all times.
As $\to A$ is a constant vector so $\nabla A = 0$ so the components of the $\to L$ in the direction of $\to A$ does not change with time.
Due to the conservation of angular momentum the magnitude of $\to L$ does not change with time.

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Similar questions

Q. The torque

τ

on a body about a given point is found to be equal to

\to A \times \to L

, where

\to A

is a constant vector and

\to L

is the angular momentum of the body about the point. From this, it follows that

τ = \frac{d \to L}{d t}

(where

L

is the angular momentum and

t

is time).
a)

\to A

is perpendicular to

\to L

at all instants of time.
b) The component of

\to L

in the direction of

\to A

does not change with time.
c) The magnitude of

\to L

does not change with time.
d)

\to L

does not change with time.

Q. The torque

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\to A \times \to L

where

\to A

is a constant vector and

\to L

is angular momentum of the body about that point. From this it follows that

Q. The torque

\to τ

on a body about a given point is found to be

\to A \times \to L

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\to L

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The torque →τ on a body about a given point is found to be equal to →A×→L where →A is a constant vector and →L is the angular momentum of the body about that point. From this it follows that :

The torque $\to τ$ on a body about a given point is found to be equal to $\to A \times \to L$ where $\to A$ is a constant vector and $\to L$ is the angular momentum of the body about that point. From this it follows that :