Torque
Physics 2
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Torque
Torque is what causes angular acceleration
(just like a force causes linear acceleration)
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Torque
Torque is what causes angular acceleration
(just like a force causes linear acceleration)
For a torque to be applied to an object, there needs to be
a force that acts at some distance away from a pivot point.
For example, consider tightening a bolt with a wrench.
Which of the 3 forces shown will tighten the bolt?
Pivot Point
FA
FC
FB
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Torque
Torque is what causes angular acceleration
(just like a force causes linear acceleration)
For a torque to be applied to an object, there needs to be
a force that acts at some distance away from a pivot point.
For example, consider tightening a bolt with a wrench.
Which of the 3 forces shown will tighten the bolt?
Pivot Point
FA
Force B will tend to rotate the bolt
clockwise, which will tighten it.
FC
FB
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Torque
Torque is what causes angular acceleration
(just like a force causes linear acceleration)
For a torque to be applied to an object, there needs to be
a force that acts at some distance away from a pivot point.
For example, consider tightening a bolt with a wrench.
Which of the 3 forces shown will tighten the bolt?
Pivot Point
FA
Force B will tend to rotate the bolt
clockwise, which will tighten it.
Notice that force A will tend to rotate the
bolt counter-clockwise, loosening it.
What does force C do?
FC
FB
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Torque
Torque is what causes angular acceleration
(just like a force causes linear acceleration)
For a torque to be applied to an object, there needs to be
a force that acts at some distance away from a pivot point.
For example, consider tightening a bolt with a wrench.
Which of the 3 forces shown will tighten the bolt?
Pivot Point
FA
Force B will tend to rotate the bolt
clockwise, which will tighten it.
Notice that force A will tend to rotate the
bolt counter-clockwise, loosening it.
What does force C do?
FC
FB
Force C doesn’t cause any rotation at all –
there is no torque generated by force C.
Why not?
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Torque
Torque is what causes angular acceleration
(just like a force causes linear acceleration)
For a torque to be applied to an object, there needs to be
a force that acts at some distance away from a pivot point.
For example, consider tightening a bolt with a wrench.
Which of the 3 forces shown will tighten the bolt?
Pivot Point
FA
Force B will tend to rotate the bolt
clockwise, which will tighten it.
Notice that force A will tend to rotate the
bolt counter-clockwise, loosening it.
What does force C do?
FC
FB
Force C doesn’t cause any rotation at all –
there is no torque generated by force C.
Why not?
Force C points directly at the pivot point –
no torque is created in this case.
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB


Torque
 
r F Direction is perpendicular to both radius and force.
 
The angle in the formula is between the force and the
r F sin( ) radius (from the pivot point to where the force is applied).
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB


Torque
 
r F Direction is perpendicular to both radius and force.
 
The angle in the formula is between the force and the
r F sin( ) radius (from the pivot point to where the force is applied).
Take a look at the diagram – r and θ are shown for force A.
FA
Pivot Point
θ
r
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB


Torque
 
r F Direction is perpendicular to both radius and force.
 
The angle in the formula is between the force and the
r F sin( ) radius (from the pivot point to where the force is applied).
Take a look at the diagram – r and θ are shown for force A.
FA
Pivot Point
There are 2 ways to interpret the formula.
•If you group the Fsin(θ) together, that represents the
component of the force that is perpendicular to the radius.
To get the most torque, the force should be applied
perpendicular (can you see why from the formula?)
θ
r
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB


Torque
 
r F Direction is perpendicular to both radius and force.
 
The angle in the formula is between the force and the
r F sin( ) radius (from the pivot point to where the force is applied).
Take a look at the diagram – r and θ are shown for force A.
FA
Pivot Point
There are 2 ways to interpret the formula.
•If you group the Fsin(θ) together, that represents the
component of the force that is perpendicular to the radius.
To get the most torque, the force should be applied
perpendicular (can you see why from the formula?)
θ
r
•The other option is to group the rsin(θ) together and call it the
“lever arm” for the force. Think of this as the shortest distance
from the pivot point to where the force is applied. This is the
effective radius of the force. Again, to get maximum torque the
angle should be 90°.
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: Find the torque of each force shown with respect
to the pivot point at the left end of the 2m long rod.
F2=30N
F1 is applied at the right end, and F2 is at the center.
120
50
F1=20N
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: Find the torque of each force shown with respect
to the pivot point at the left end of the 2m long rod.
F2=30N
F1 is applied at the right end, and F2 is at the center.
120
50

1

(2m) (20N) sin(50 )
30.6N m
F1=20N
The direction of this torque is into the page (use the right-hand-rule).
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: Find the torque of each force shown with respect
to the pivot point at the left end of the 2m long rod.
F2=30N
F1 is applied at the right end, and F2 is at the center.
120
50

1

(2m) (20N) sin(50 )
30.6N m
F1=20N
The direction of this torque is into the page (use the right-hand-rule).

2
(1m) (30N) sin(120 )
26.0N m
The direction of this torque is out of the page (use the right-hand-rule).
Note that the angle could also be 60° and we get the same answer.
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Torque
We mentioned earlier that torques produce angular
accelerations. We have a formula for this relationship:
I
This is really just Newton’s 2nd law applied to rotational
motion. The moment of inertia, I, takes the place of the
mass, and we use angular acceleration instead of linear.
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: Find the angular acceleration of the 2m long, uniform
rod (mass=5kg) when it is subject to the 2 forces shown.
F2=30N
F1 is applied at the right end, and F2 is at the center.
120
50
F1=20N
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: Find the angular acceleration of the 2m long, uniform
rod (mass=5kg) when it is subject to the 2 forces shown.
F2=30N
F1 is applied at the right end, and F2 is at the center.
120
We will need to find the moment of inertia for this rod.
From our table of shapes (p.299 in textbook) we find a formula:
I
1 ML2
3
I
1 (5kg)(2m)2
3
50
F1=20N
6.67kg m2
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: Find the angular acceleration of the 2m long, uniform
rod (mass=5kg) when it is subject to the 2 forces shown.
F2=30N
F1 is applied at the right end, and F2 is at the center.
120
50
We will need to find the moment of inertia for this rod.
F1=20N
From our table of shapes (p.299 in textbook) we find a formula:
I
1 ML2
3
I
1 (5kg)(2m)2
3
6.67kg m2
Now we can apply our torque formula. We’ll define positive torque to mean
“out of the page”. Alternately you can think of this as “counter-clockwise”.
We can put a little arrow symbol to indicate this in the diagram.
+
With this choice torque 1 is negative, and torque 2 is positive.
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: Find the angular acceleration of the 2m long, uniform
rod (mass=5kg) when it is subject to the 2 forces shown.
F2=30N
F1 is applied at the right end, and F2 is at the center.
120
50
We will need to find the moment of inertia for this rod.
F1=20N
From our table of shapes (p.299 in textbook) we find a formula:
I
1 ML2
3
I
1 (5kg)(2m)2
3
6.67kg m2
Now we can apply our torque formula. We’ll define positive torque to mean
“out of the page”. Alternately you can think of this as “counter-clockwise”.
We can put a little arrow symbol to indicate this in the diagram.
+
With this choice torque 1 is negative, and torque 2 is positive.
I
30.6N m
26.0N m
6.67kg m2
0.69 ras d
The negative sign means that the angular acceleration vector points into
the page, and the object’s will accelerate in the clockwise direction.
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB