In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment, moment of force, rotational force or turning effect, depending on the field of study. The concept originated with the studies by Archimedes of the usage of levers. Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object around a specific axis. Another definition of torque is the product of the magnitude of the force and the perpendicular distance of the line of action of a force from the axis of rotation. The symbol for torque is typically
τ
{\displaystyle {\boldsymbol {\tau }}}
or τ, the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M.
In three dimensions, the torque is a pseudovector; for point particles, it is given by the cross product of the position vector (distance vector) and the force vector. The magnitude of torque of a rigid body depends on three quantities: the force applied, the lever arm vector connecting the point about which the torque is being measured to the point of force application, and the angle between the force and lever arm vectors. In symbols:
{\displaystyle \tau =\|\mathbf {r} \|\,\|\mathbf {F} \|\sin \theta \,\!}
where
τ
{\displaystyle {\boldsymbol {\tau }}}
is the torque vector and
τ
{\displaystyle \tau }
is the magnitude of the torque,
r
{\displaystyle \mathbf {r} }
is the position vector (a vector from the point about which the torque is being measured to the point where the force is applied),
F
{\displaystyle \mathbf {F} }
is the force vector,
×
{\displaystyle \times }
denotes the cross product, which produces a vector that is perpendicular to both r and F following the right-hand rule,
θ
{\displaystyle \theta }
is the angle between the force vector and the lever arm vector.The SI unit for torque is the newton-metre (N⋅m). For more on the units of torque, see § Units.
Good morning,
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This was how the solution was arrived in the text,
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0 = 2mg x 2R x sin ϴ0 + m x R x sinϴ0 - T R
T = 5 mg sinϴ0
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m(rod) * 9.8 + m(LB) * 9.8 + m(RB) * 9.8 = 137 N
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Homework Statement
[/B]
Homework Equations
Drawing a diagram for the forces is the easy part. I am not sure I am doing the equation of the sum of the torques well.
The Attempt at a Solution
This is my attempt for the forces[/B]
And this for the torques:
Homework Statement
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Homework Statement
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Homework Statement
Find the period of small oscillation of this system.
Homework Equations
3. The Attempt at a Solution
[/B]
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Homework Statement
[/B]
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In a pump (which operates in normal condition: steady state), pump torque is positive and fluid torque is of equal magnitude and of opposite direction so that the sum of both is zero. ''P. 66 of 'Water Hammer: An Analysis of Plumbing Systems, Intrusion, and Pump Operation' by: Dr. Loganathan...
Homework Statement
Homework Equations
ok, I thought that the torque from the mass 'm' would be equal to torque from mass 'M'
The Attempt at a Solution
I wrote down:
m * g * (d/4) = M * g * d
(m/4) = M
m = 4M
Thus, the ratio is 4M : 1 m, which gives answer 1.
However, the solutions say...
1. Homework Statement
problem is above
Homework Equations
sum of torques = I * angular acceleration = 0 for rotational equilibrium
The Attempt at a Solution
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1. Homework Statement
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Homework Statement
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Homework Statement
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Homework Statement
Homework Equations
Torque=one of the forces x the perpendicular distance
moment=force x perpendicular distance
The Attempt at a Solution
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Homework Statement
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Homework Statement
A 10.0kg sphere is attached to the incline by a horizontal string. Determine the tension in the string.
Homework Equations
(F⃗ net)x=ΣFx=0
(F⃗ net)y=ΣFy=0
Στ=0
τ = (radial disance)(F)
The Attempt at a Solution
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$$
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$$
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Homework Statement
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Homework Statement
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Homework Statement
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Homework Statement
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Hi,
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Homework Statement
A square metal plate 0.180 m on each side is pivoted about an axis through point O at its center and perpendicular to the plate (Figure 1) .
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Homework Statement
Answer: C
Note: Sorry admins for the picture, needed to include the diagram though.
Homework Equations
∑\tau = I\alpha
∑F = ma
a = \alphar
The Attempt at a Solution
The torques must be balanced (is this reasoning already wrong?), thus,
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F_T =...
Homework Statement
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Homework Statement
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