Respuesta :
Answer:
a) τ =0, b) τ = 4.0 N m , c) τ = 2 / √t, d) τ = 2 t N m
Explanation:
Angular momentum and torque are related by the equation.
τ =dL / dt
Bold indicates vectors, as time is a scalar, the direction of L is the same as the direction of the torque
Let's analyze each case presented
a) L = 4.0 kg m2 / s
As L is constant
dL / dt = 0
τ= 0
b) L = 4 t
dL / dt = 4
τ = 4.0 N m
c) L = 4 √ t
dL / dt = 4 ½ 1/√t = 2 / √ t
τ = 2 / √ t
d) L = 4 t²
dL / dt = 4 (2t)
τ = 2 t N m
The torques are as given below:
(a) 0
(b) 8t Nm
(c) 2/[tex]\sqrt{t}[/tex] Nm
(d) -8/t³ Nm
Torque:
The torque acting on a body is defined as the rate of change of angular momentum, mathematically it is expressed as follows:
[tex]\tau=\frac{dL}{dt}[/tex]
where L is the angular momentum of the body.
(a) L = 4 kgm²/s
then torque is:
[tex]\tau=\frac{dL}{dt}=0[/tex]
when the angular momentum is constant, the torque acting on a body is zero.
(b) L = 4t² kgm²/s
then, torque is:
[tex]\tau=\frac{dL}{dt}=\frac{d}{dt}(4t^2)\\\\\tau=8t \;Nm[/tex]
(c) L = 4√t kgm²/s
then, torque is:
[tex]\tau=\frac{dL}{dt}=\frac{d}{dt}(4\sqrt{t} )\\\\\tau=\frac{2}{\sqrt{t} } \;Nm[/tex]
(d) L = 4/t² kgm²/s
then, torque is:
[tex]\tau=\frac{dL}{dt}=\frac{d}{dt}\frac{4}{t^2}\\\\\tau=\frac{-8}{t^3} \;Nm[/tex]
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