LESSON 1.16 - ROTATION
Overview
This lesson deals with rotational forces, rotational
inertia and angular momentum. On completion of the
lesson, you should be able to calculate the torque
applied to an object and the angular momentum of a
rotating object. You should also be able to discuss some
of the factors that affect rotational inertia.
ACTIVITIES
- Measure the torques
produced on a bicycle wheel using different gear
settings.
- Compare the torques
produced by two different electric motors or
appliances.
Turning Forces
When an object or body rotates, angular acceleration or
changes in rotational speed are caused by turning forces
or moments acting away from the axis of rotation. The
torque or moment is a measure of the ability of a force
to cause an object to rotate. The torque is the magnitude
of the tangential force multiplied by its distance from
the axis of rotation.
Tangential Force
The force causing rotation needs to act perpendicular to
a line from the axis to the point at which the force is
applied. If r is the distance from the axis to the
point at which the force is applied and a circle with
radius r is drawn around the point of rotation,
the force needs to act at a tangent to this circle.
Rotational Inertia
Inertia is the tendency of a body to oppose acceleration.
The tendency of a body to oppose rotational acceleration
is known as its rotational inertia. Rotational inertia
depends on the distribution of the mass of the body in
relation to the center of rotation. Two objects with the
same mass can have different quantities of rotational
inertia if their masses are distributed differently. A
ring with the same mass as a coin will have a greater
rotational inertia.
Angular momentum
This is the momentum a body has as a result of its
rotational motion. It is the product of the mass, the
average distance of the mass from the axis and the
tangential speed of the mass.
Example 1.16.1 Torque
A spring balance attached
to the end of a wrench is used to set the torque on a nut.
If the spring balance is attached to the wrench is 30 cm
from the center of the nut and the force applied
perpendicular to the wrench is 3.5 N, what is the torque
applied to the nut?
Solution
The distance from the
point of rotation to the force is 30 cm or 0.3 m.
The torque is therefore 3.5
N x 0.3 m
Torque = 1.05 N-m.
Example 1.16.2 Angular
Momentum
A ring-shaped space
station has an average radius of 30 m and a mass of 900,000
kilograms. If it rotates at 4 revolutions per minute,
what is its angular momentum?
Solution
If the space station’s
radius is 30 m, its average circumference = 2 x p x 30 m which
= 188.5 m.
The tangential speed of
this mass is 3 x 188.5 m/minute or 565.5 m/min.
Divide 565.5 m/min by 60
to give 9.425 m/s.
The angular momentum is
thus 900,000 kg x 9.425 m/s x 30 m.
This equals 2.55 x108
kg.m2/s
Review
Questions
- Most motorcycles use
a chain to transfer energy from the motor to the
rear wheel. Some types of motorcycle have a
driveshaft instead of a chain. What type of force
is transferred through a driveshaft?
- Motor vehicles with
disk brakes have metal disks attached to the
wheel hubs. When the brakes are applied, firmly
mounted pads clamp onto the disks and apply
friction to the disks. Does this friction apply
torque to the wheels?
- The diagram below
shows a wrench with three forces A, B and C
acting on the wrench. Each of these forces can
cause rotation. Which force is acting
tangentially?
- Two bicycle wheels
with the same mass have diameters of 0.6 m and 1.0
m respectively.
Which wheel can be expected to have the greater
rotational inertia?
- Two people are
sitting on identical office chairs that can
swivel easily. One has his arms extended, the
other has his arms folded. With their feet off
the ground in similar positions, which person has
the greater rotational inertia?
- The diagram below
shows a ruler that is balanced at point A.
Neglecting the weight of the ruler, what is the
clockwise moment acting on the ruler?
What force is acting downwards on the left-hand
side of the ruler?
The diagram below shows a ruler that is balanced
at point A.
Neglecting the weight of the ruler, what is the
clockwise moment acting on the ruler?
What is the mass suspended on the left hand side
of the ruler?
A Scottish hammer thrower swings a steel ball
with a mass of 20kg in a circular path. The path
has a radius of 1.5 meters and the ball rotates
around the thrower at a rate of 0.7 revolutions
per second.
What is the tangential velocity of the ball?
What is the angular momentum of the ball?
ACTIVITIES
- Measure the torques
produced on a bicycle wheel using different gear
settings.
- Compare the torques
produced by two different electric motors or
appliances.
ACTIVITY
#1 Bicycle Wheel Torques
Purpose: To show
how gears affect the torque produced by the chain on a
bicycle wheel
Equipment:
Bicycle
Spring balance
Tape measure
Stand to keep rear wheel
of bicycle off the ground.
Procedure:
- Mount the bicycle in
such a way that the rear wheel of the bicycle can
turn freely.
- Attach a spring
balance to the outer end of one of the spokes on
the wheel.
- Note the gear setting
on the bicycle and push hard on one of the pedals.
- Measure the force
exerted by the spoke on the spring balance.
Ensure that the force is measured perpendicular
to the spoke.
- Calculate the torque
by multiplying the force by the distance of the
end of the spring balance from the center of the
wheel.
- Change the gear
setting on the wheel sprocket and repeat the
experiment.
Question
- Is there a
relationship between the number of teeth on the
sprocket and the measured torque?
ACTIVITY
#2 Electric Motor Torques
Purpose: To
illustrate the torques produced by different electric
motors.
Equipment:
Various battery-powered
electric motors
If possible, open up an
old camera and remove the rewind motor. (Thrift stores
often have old cameras for $1 or less. The lenses and
shutter mechanisms will be useful when we study light.)
Procedure:
- Be careful to use
only weak battery-powered motors.
- Run the motors and
see how easy it is to stop each motor by holding
a piece of wood against the spinning part.
Question
How do the gears inside
some of the motors increase the torque?
.
.
HANDS-ON
HOMEWORK
Select one or more of the recommended
activities for Lesson 2.1, collect the items needed and test the
procedure before demonstrating the activity during the
next theory lesson.
Lesson 1.15
Machines
- Yes, machines
are devices that are used to multiply forces or
change the direction of forces.
- 7.5
- The mechanical
advantage of the system (lever) is 7.5. The
effort – or downward force – needs to
move 7.5 times as far as the load moves. If the
load moves 200cm, the other end of the lever must
move 7.5 x 200cm = 1500cm or 1.5 meters.
-
The actual
mechanical advantage is always a bit less as a
result of energy losses due to friction. - The efficiency of a
machine is the ratio of the work output to the
work input. The loss of energy due to friction
results in a decrease in efficiency.
- There are two movable
pulleys in the system. The mechanical advantage
is therefore 2 x 2 = 4.
- The rock moves 6
meters in order to gain 3 meters. The mechanical
advantage is 6/3 = 2.
- The circumference of
the screw is p x 0.02m = 0.0628m
If the screw
is rotated 50 times, the distance traveled up the
inclined plane (thread) is 50 x 0.0628m
This = 3.14 meters. The height gained as a result
of this is 0.2 meters.
The mechanical advantage is thus = 3.14 / 0.2 = 15.7
|
