Why are torque and angular momentum considered vectors?
Why are torque and angular momentum considered vectors?
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]
By conservation of Angular momentum
Li = Lf

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
Kindly consider the following Image
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
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