Net Torque & Sign of Torque Video Lessons

Concept

Problem: 1.) Which of the following statements is correct when the net torque on an object is non-zero?a) The angular velocity of the object is constantb) The angular velocity of the object is changingc) The net force is always non-zero2.) Which of the following statements is true when the net force and net torque on an object is zero?a) The object is always at unstable equilibriumb) The object is always at equilibriumc) The object is always at stable equilibrium

FREE Expert Solution

1)

Net torque:

$\overline{){{\mathbf{N}}}^{\mathbf{\left(}\mathbf{e}\mathbf{\right)}}{\mathbf{=}}\frac{\mathbf{d}\mathbf{L}}{\mathbf{d}\mathbf{t}}}$

$\begin{array}{rcl}\frac{\mathbf{dL}}{\mathbf{dt}}& \mathbf{=}& \frac{\mathbf{d}}{\mathbf{d}\mathbf{t}}\mathbf{r}{\mathbf{F}}^{\mathbf{\left(}\mathbf{e}\mathbf{\right)}}\\ & \mathbf{=}& \frac{\mathbf{d}}{\mathbf{dt}}\mathbf{\left(}\mathbf{r}\mathbf{×}\mathbf{p}\mathbf{\right)}\mathbf{=}\frac{\mathbf{d}}{\mathbf{dt}}\mathbf{\left(}\mathbf{r}\mathbf{×}\mathbf{mv}\mathbf{\right)}\\ & \mathbf{=}& \mathbf{m}\frac{\mathbf{d}}{\mathbf{dt}}\mathbf{\left(}\mathbf{r}\mathbf{×}\mathbf{v}\mathbf{\right)}\\ & \mathbf{=}& \mathbf{m}\frac{\mathbf{d}}{\mathbf{dt}}\mathbf{\left(}\mathbf{r}\mathbf{×}\mathbf{r\omega }\mathbf{\right)}\end{array}$

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Problem Details

1.) Which of the following statements is correct when the net torque on an object is non-zero?

a) The angular velocity of the object is constant

b) The angular velocity of the object is changing

c) The net force is always non-zero

2.) Which of the following statements is true when the net force and net torque on an object is zero?

a) The object is always at unstable equilibrium

b) The object is always at equilibrium

c) The object is always at stable equilibrium

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