5.2 Torque and Rotational Statics

• What force $F_{2}$ is required at $r_{2} =$$2 \text{ m}$ to balance $F_{1} =$$20 \text{ N}$ at $r_{1} =$$1 \text{ m}$?


  10 N
• To maintain rotational equilibrium, a force of 10 N must be applied at the second location
• The torque formula is $τ =$$rF_\perp$, where $F_\perp$ is the perpendicular component of the force.


  True
• What is the perpendicular force when a 50 N force is applied at a 30° angle?

  25 N
• For rotational static equilibrium, the sum of all torques must be zero.


  True
• Steps to solve rotational statics problems:

  1️⃣ Identify all forces and their distances from the pivot point

  2️⃣ Resolve forces into perpendicular components

  3️⃣ Calculate each torque

  4️⃣ Apply the equilibrium condition

  5️⃣ Solve for any unknowns
• What is torque?

  Rotational force
• What is rotational static equilibrium?

  No net torque
• What is the formula for the magnitude of torque using the lever arm, force, and angle?

  $\tau =$$rF\sin{\theta}$
• The angle $\theta$ in the torque formula is the angle between the lever arm and the force.


  True
• What determines the magnitude and direction of torque?

  Lever arm, force, angle
• What is the direction of torque in relation to the lever arm and force?

  Perpendicular to both
• Steps to determine the direction of torque using the right-hand rule

  1️⃣ Point your fingers in the direction of the lever arm $\vec{r}$.

  2️⃣ Curl your fingers towards the direction of the force $\vec{F}$.

  3️⃣ Your thumb points in the direction of the torque $\vec{\tau}$.
• The direction of torque is perpendicular to both the lever arm and the force.


  True
• The right-hand rule is used to determine the direction of torque.


  True
• Torque is the rotational force that causes an object to rotate
• The formula for torque as a cross product is \vec{\tau} = \vec{r} \times \vec{F}</latex>.


  True
• The right-hand rule can be used to determine the direction of torque in the cross product formula.

  True
• Torque is a vector quantity with both magnitude and direction.


  True
• In rotational static equilibrium, clockwise torques are equal to counterclockwise torques.


  True
• What is the condition for rotational static equilibrium in mathematical form?

  $\sum \tau =$$0$
• What does rotational static equilibrium mean in terms of object movement?

  Object is not rotating
• The condition for rotational static equilibrium is that clockwise torques must equal counterclockwise torques

  True
• What force $F_{2}$ is required at a distance of $2 \text{ m}$ to achieve rotational static equilibrium if $F_{1} =$$20 \text{ N}$ is applied at $1 \text{ m}$?


  $10 \text{ N}$
• Torque is a vector quantity with both magnitude and direction


  True
• How is the direction of torque determined?

  Right-hand rule
• The right-hand rule is used to determine the direction of torque


  True
• Torque is a vector quantity with both magnitude and direction.
• The direction of torque is always perpendicular to both the lever arm and the force


  True
• Steps to achieve rotational static equilibrium

  1️⃣ Ensure no rotation occurs

  2️⃣ Sum of all torques is zero

  3️⃣ Clockwise torques equal counterclockwise torques
• Torque is a scalar quantity.

  False
• If a force of 10 N is applied at a lever arm of 0.5 m with an angle of 90 degrees, the torque is 5 Nm.
• The condition for rotational static equilibrium is \sum \tau = 0
• What is the condition for linear equilibrium?

  $\sum F =$$0$
• Steps to solve rotational statics problems

  1️⃣ Identify all forces and their lever arms relative to the pivot point

  2️⃣ Resolve forces into perpendicular and parallel components

  3️⃣ Set up the equation $\sum \vec{\tau}_{\text{clockwise}} =$$\sum \vec{\tau}_{\text{counterclockwise}}$

  4️⃣ Solve for the unknown variable
• What is the formula for torque?

  \tau = rFsinθ</latex>
• What is torque defined as?

  Rotational force
• The magnitude of torque is determined by the formula: τ = rFsinθ
• What is the torque if a force of 20 N is applied at a lever arm of 0.5 m and the angle between them is 90°?

  10 Nm
• The vector formula for torque is: \vec{\tau} = \vec{r} \times \vec{F}