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

Can an object have angular momentum without torque?

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Answered by

Syed Aquib Ur Rahman | Contributor-Level 10

2 months ago

Yes, an object can have angular momentum without torque. The physics behind it is that if no external force act on an object, its angular momentum is constant. That is based on the law of conservation of momentum.

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By conservation of Angular momentum

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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)?
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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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