Solved Examples of Torque: Step-by-Step Solutions for Physics

📚 Quick Study Guide

• 📏 Definition: Torque ($\tau$) is the rotational equivalent of linear force. It measures the force that can cause an object to rotate about an axis.
• 🧮 Formula: The magnitude of torque is given by $\tau = rF\sin(\theta)$, where:
  • $r$ is the length of the lever arm (the distance from the axis of rotation to the point where the force is applied).
  • $F$ is the magnitude of the force.
  • $\theta$ is the angle between the force vector and the lever arm.
• 🧭 Direction: Torque is a vector quantity. Its direction is perpendicular to both the lever arm and the force, following the right-hand rule.
• ➕ Net Torque: If multiple torques act on an object, the net torque is the vector sum of all individual torques. $\tau_{net} = \tau_1 + \tau_2 + ...$
• ⚙️ Equilibrium: An object is in rotational equilibrium when the net torque acting on it is zero.

Practice Quiz

1. A wrench is used to tighten a bolt. A force of 50 N is applied at a distance of 0.2 m from the center of the bolt. If the angle between the wrench and the force is 90 degrees, what is the magnitude of the torque applied to the bolt?
   1. 1 Nm
   2. 5 Nm
   3. 10 Nm
   4. 25 Nm
2. A seesaw is balanced with two children sitting on it. Child A weighs 300 N and sits 1.5 m from the pivot. Child B sits 2 m from the pivot. What is the weight of Child B for the seesaw to be balanced?
   1. 150 N
   2. 200 N
   3. 225 N
   4. 450 N
3. A door requires a torque of 12 Nm to open. If you push on the door 0.8 m from the hinges, what force must you apply perpendicular to the door?
   1. 9.6 N
   2. 15 N
   3. 12.8 N
   4. 10 N
4. A wheel with a radius of 0.3 m has a force of 20 N applied tangentially to its edge. What is the torque produced?
   1. 6 Nm
   2. 6.7 Nm
   3. 0.6 Nm
   4. 20.3 Nm
5. A meter stick is pivoted at the 50 cm mark. A 2 N weight is hung at the 20 cm mark. Where must a 3 N weight be hung to balance the meter stick?
   1. 70 cm
   2. 80 cm
   3. 60 cm
   4. 90 cm
6. A rod is 2 m long and pivoted at its center. A force of 10 N is applied at one end at an angle of 30 degrees to the rod. What is the magnitude of the torque?
   1. 5 Nm
   2. 8.66 Nm
   3. 10 Nm
   4. 17.32 Nm
7. Two forces are applied to a circular disc of radius 0.5 m. Force F1 = 5 N is applied at the edge, and force F2 = 3 N is applied at a point 0.2 m from the center. Both forces are tangential. What is the net torque on the disc?
   1. 1.9 Nm
   2. 3.1 Nm
   3. 2.5 Nm
   4. 0.6 Nm