LECTURE 21
TORQUE
Instructor: Kazumi Tolich
Lecture 21
2
¨
Reading chapter 11-1 to 11-2
¤ Torque
¤ Newton’s
2nd law for rotation
Torque about an axis
3
¨
Torque (𝜏) is a measure of twisting, and the magnitude of
torque is defined as
𝐅⃗
𝜏 = 𝑟𝐹 sin 𝜃 = 𝐹) 𝑟 = 𝐹𝑟*
¨
¨
¨
𝑟* is called moment arm, or lever arm of 𝐅⃗.
The SI unit for torque is N·∙m, the same as the unit of work. But
torque and work are different physical quantities.
If two or more torques act on a rigid object, the net torque is
the sum of the torques with correct sign assigned to each
torque.
𝜃
𝐅⃗)
𝐫⃗
Axis
𝑟*
Line of action
Newton’s 2nd law for rotation
4
¨
Newton’s 2nd law for rotation is given by
. 𝜏 = 𝐼𝛼
¨
¨
The sign of torque is the same as the sign of angular acceleration it
causes if it were the only torque acting in the system.
This is analogous to Newton’s 2nd law for linear motion: ∑ 𝐅⃗ = 𝑚𝐚
Quiz: 1
5
Door knobs
6
¨
Why are all door knobs located farthest from the door hinges?
¤ It
gives the longest moment arm, and therefore the most torque, assuming
the knobs are always pushed normal to the door.
¤ The more torque you give, the more rotational acceleration of the door you
get.
Demo: 1
7
¨
Torque Bar
¤ Demonstration
of lever arm dependence of torque
Quiz: 2 & 3
8
Example: 1
9
¨
At the local playground, a child with a
mass 𝑚 = 16 kg sits on the end of a
horizontal teeter-totter, a distance of
𝐿 = 1.5 m from the pivot point. On the
other side of the pivot an adult pushes
straight down on the teeter-totter with a
force of 𝐹 = 95 N. In which direction does
the teeter-totter rotate if the adult applies
the force at a distance of
a)
b)
c)
𝐿6 = 3.0 m,
𝐿6 = 2.5 m,
or 𝐿6 = 2.0 m from the pivot?
Quiz: 4
10
Demo: 2
11
¨
Hinged Stick and Ball
¤ When
the bar is just about to become horizontal, the acceleration of the
free-end of the bar is greater than 𝑔.
¤ 𝛼
¤ 𝑎
8
9
<
:;=
= =>
A;
= B@
=
:@
?
= 𝐿𝛼 =
A;
B
>𝑔
Example: 2
12
¨
Figure shows the massive shield door at a neutron
facility at Lawrence Livermore National
Laboratory; this is the world’s heaviest hinged
door. The door has a mass of 𝑀 = 44,000 kg, a
rotational inertia about an axis through its hinges
of 𝐼 = 8.7 × 104 kgŸm2, and a front face width
of 𝑤 = 2.4 m. Neglecting friction, what steady
force, applied at its outer edge and
perpendicular to the plane of the door, can move
it from rest through an angle of 𝜃 = 90º in
𝑡 = 30 s?
Example: 3
13
¨
A wheel on a game show is given an initial
angular speed of 𝜔I = 1.22 rad/s. It
comes to rest after rotating through
∆𝜃 = 0.75 of a turn.
a)
b)
Find the average torque exerted on the
wheel given that it is a disk of radius
𝑟 = 0.71 m and mass 𝑚 = 6.4 kg.
If the mass of the wheel is doubled, and its
radius is halved, will the angle through
which it rotates before coming to rest
increase, decrease, or stay the same
assuming that the average torque exerted
on the wheel is unchanged?