What is torque and how does it relate to angular momentum?
What is torque and how does it relate to angular momentum?
Torque is the measure of rotational force on an object (rigid or extended body). It changes the object's angular momentum. To calculate in physics, torque equals the rate of change of angular momentum. The formula for that is
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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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