Torque A PowerPoint Presentation by

Paul E. Tippens, Professor of Physics

Southern Polytechnic State University

© 2007 Edited by Miss Espina, 2014

Warm up:

1. Take out your notebook/binder for notes

2. Where have you heard the term ‘torque’ before?

Torque is a twist or turn that tends to produce rotation. * Applications are found in many common tools around the home or industry where it is necessary to turn, tighten or loosen devices.

Definition of Torque

Torque is defined as the tendency to produce a change in rotational motion.

Examples:

Car engine torque

240 ft lb of torque = 325.4 Nm

A Ford F -150 has up to 860 ft lbs of Torque!

Torque is Determined by Three Factors:

• The magnitude of the applied force.

• The direction of the applied force.

• The location of the applied force.

20 N

Magnitude of force

40 N

The 40-N force produces twice the torque as does the

20-N force.

Each of the 20-N forces has a different

torque due to the direction of force. 20 N

Direction of Force

20 N

θ θ

20 N 20 N

Location of force The forces farther away from the pivot point have greater

torques. 20 N 20 N

Units for Torque Torque is proportional to the magnitude of F and to the distance r from the axis. Thus, a formula might be:

τ = Fr Units: N⋅m

6 cm 40 N

τ = (40 N)(0.06 m)

= 2.40 N⋅m

τ = 2.40 N⋅m

Work vs. Torque

• If Work and Torque have the same formula, why are they measured in different units?

• Torque is a cross-product which uses the perpendicular part of the force and produces a different motion. The formulas are actually different and mean different things

Direction of Torque

Torque is a vector quantity that has direction as well as magnitude.

Turning the handle of a screwdriver clockwise and then counterclockwise will

advance the screw first inward and then outward.

Sign Convention for Torque By convention, counterclockwise torques are positive and clockwise torques are negative.

Positive torque: Counter-clockwise,

out of page

cw

ccw

Negative torque: clockwise, into page

Lever Arm distance

The r of the Torque equation is the perpendicular distance from the point of application of a force to the axis of rotation.

Calculating Torque • Read problem and draw a rough figure.

• Draw the force vectors (arrows).

• Draw and label lever arm distance.

• Apply definition of torque:

τ = Fxr Torque = (force) (lever arm distance) sin θ

Conceptual question

• Keeping in mind the equation for torque, does it require more force to open a door by pushing it close to the hinge or far from the hinge?

Example 1 (single force)

• Calculate the torque produced by a 75 N perpendicular force acting at the end of a 0.3-m long wrench.

Example 2: (torque with force at an angle) An 80-N force acts at the end of a 12-cm wrench as shown. Find the torque.

Note from figure: r = 12 cm τ = (69.3 N)(0.12 m)

τ =(80 N) (0.12 m) sin (60) τ = 8.31 N m

12 cm

Calculating Resultant Torque • Read, draw, and label a rough figure.

• Draw free-body diagram showing all forces, distances, and axis of rotation.

• Calculate torques due to EACH individual force affixing proper sign. CCW (+) and CW (-).

• Resultant torque is sum of individual torques.

Example 3 (two torques)

• Two kids are playing on a seesaw. One of the kids weighs 100N and sits 1m from the fulcrum. The second kid weighs 200N. How far away from the fulcrum must the second kid sit to balance the seesaw?

Example 4 (equilibrium example)

• Suppose a meter stick is suspended from the ceiling by a string from its center. A 10 N block is hung at the 80 cm mark. Another block of unknown weight balances the system when it is hung at the 10 cm mark. What is the weight of this block?

Example 5

• Julia is given two weights and a meter stick. She is told that he must hang the weights on the meter stick and balance the meter stick. If one weight is 1.47N (150g) and hung 0.2m from the balance point, how far away from the balance point must Julia hang a second weight that weighs 1.96N (200g)?

Example 6 • Alex is given two weights and a meter

stick. She is told that he must find the weight of a second block by balancing two blocks on a meter stick. If one block of 20N is hung at the 80cm mark and the second block is hung at the 10cm mark, what does the second block weigh?

Example 7 (equilibrium example)

• A window washer is standing on a scaffold supported by vertical ropes at each end. The scaffold weighs 200. N and is 3.00 m long. What is the tension in each rope when the 700. N worker stands 1.00 m from one end?

Summary Torque is the cross product (add sin θ) of a

force and its lever arm distance

τ = F x r

τ = F r sin θ Torque = (force) (lever arm

distance) sin θ

Summary: Resultant Torque • Read, draw, and label a rough figure.

• Draw free-body diagram showing all forces, distances, and axis of rotation.

• Calculate torques due to EACH individual force affixing proper sign. CCW (+) and CW (-).

• Resultant torque is sum of individual torques.

CONCLUSION: Chapter 5A Torque