Why are torque and angular momentum considered vectors?

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Both torque and angular momentum have direction. We determine their direction based on the right-hand rule. That makes them vector quantities in rotational motion. 

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Angular impulse = Change in angular momentum

[J] = [mvr]

[J] = [M1L2T–1]

Position vector about O (r_o) = 5i + 5√3j

Force vector (F) = 4i - 3j

Torque about O (τ_o) = r_o × F
τ_o = (5i + 5√3j) × (4i - 3j)
τ_o = -15k - 20√3k = (-15 - 20√3)k

Position vector about Q (r_q) = -5i + 5√3j

Torque about Q (τ_q) = r_q × F
τ_q = (-5i + 5√3j) × (4i - 3j)
τ_q = 15k - 20√3k = (15 - 20√3)k

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
⇒ 50αβt² k? - 100αβt (t-5) k? = 0
⇒ 50t² - 100t (t-5) = 0
⇒ 50t² - 100t² + 500t = 0
⇒ -

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Physics System of Particles and Rotational Motion 2025

Physics System of Particles and Rotational Motion 2025

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