Physics 12 Notes on Rotational Equilibrium. Name:______

WHAT IS TORQUE?

Torque is a measure of how much a force acting on an object causes that object to rotate. The object rotates about an axis, which we will call the pivot point, and will label 'O'. We will call the force 'F'. The distance from the pivot point to the point where the force acts is called the moment arm, and is denoted by 'r'. Note that this distance, 'r', is also a vector, and points from the axis of rotation to the point where the force acts. (Refer to Figure 1 for a pictoral representation of these definitions.)

Torque is defined as

= r x F∟

Examples of calculating torques.

Example 1) Calculate the torque generated by a wrench if a 25 N force is exerted 0.35 m from the bolt as shown in the diagram?

Example 2) A 3.5 m uniform concrete beam (m = 1200 kg) is hinged at one end on the wall as shown in the diagram below. In the beam is horizontal, what is the torque the beam generated around the hinge?

More Examples on Concept of “Torque” Name:______

  1. Calculate the torque (magnitude and direction) about point O due to the force F in each of the situations sketched below. In each case, the object to which the force is applied has a length of 2.0 m and the force is 50 N.
  1. Calculate the weight of the uniform beam subjected to the forces shown below. The beam is in rotational equilibrium. 20.8 N
  1. A bowler holds a bowling ball whose mass is 7.2 kg in the palm of his hand. The upper arm is vertical and his lower arm is horizontal. What forces must the biceps muscle and the bony structure of the upper arm exert on the lower arm? The forearm and hand together have a mass of 1.8 kg. The ball is 33 cm from the elbow; the center of mass of the lower arm is 15 cm from the elbow; and the point of insertion (where the biceps muscle attaches to the lower arm) is 4 cm from the elbow. The elbow serves as the pivot. 648.27 N
  1. A uniform bar 3 m long and weighing 6 N is attached by a hinge to a wall as shown below. A 5 N weight is attached to its end. An unknown force is applied at its end at the angle shown below. What is the magnitude of the unknown force? What is the value of R, the force with which the wall pushes on the bar? 12.45 N; 10.0 N

5. Torque is used to determine the weight of an object. A 10 m long pole, weighing 20 N, has its center of gravity 2 m from one end. An object of unknown weight is hung at the end opposite the center of gravity. With the object hanging at this end, the pole now balances 2 m from the unknown weight. What is the weight of the unknown weight? 60 N

6. A 10 m long pole balances at its center. A 20 N force is applied upward at one end. A 35 N weight is hung 3 m from this 20 N force. A 40 N force is applied upward at the other end. What is the magnitude of the unknown weight that is hanging 2 m from the 40 N force that causes equilibrium? 56.67 N

  1. A 24 kg beam of length 2.4 m leans against a smooth wall. A horizontal rope tied to the wall and the beam holds the beam on a frictionless floor as shown.

a) Draw a labeled FBD for the forces acting on the beam.

b) What is the tension in the rope?