Torque and Angular Momentum Physics System of Particles and Rotational Motion Physics Class 11th

What is the significance of the direction in torque and angular momentum?

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Syed Aquib Ur Rahman | Contributor-Level 10

2 months ago

The direction of torque and angular momentum defines how and in which orientation an object will rotate or sustain its spin. This is important to understand in machines, athletic movements, and even natural phenomena, such as planetary motion.

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The dimensions of angular impulse is equal to

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Angular impulse = Change in angular momentum

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[J] = [M¹L²T^–1]

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By conservation of Angular momentum

Li = Lf

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Kindly consider the following Image

A particle of mass 'm' is moving in time 't' on a trajectory given by r? = 10αt² i? + 5β(t-5) j?. Where α and β are dimensional constants. The angular momentum of the particle become the same as it was for t = 0 at time t = ______ seconds.

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r? = 10αt²î + 5β (t-5)?
v? = dr? /dt = 20αtî + 5β?
As L? = m (r? × v? )
So, at t=0, L=0
given L is same at t=t as at t=0
⇒ r? × v? = 0
⇒ (10αt²î + 5β (t-5)? ) × (20αtî + 5β? ) = 0
⇒ 50αβt² (î×? ) + 100αβt (t-5) (? ×î) = 0
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