Download Rotation

Rotation
Name :
Level : Physics I
Date :
Teacher : Kim
►Review in Speed in Linear Motion
 The speed of an object moving in a straight line is expressed as
v=
 The speed in a straight line motion can be better expressed as linear speed
► Tangential Speed
 The speed of an object moving in a circular motion is expressed as
vT =
and is called tangential speed and the symbol is expressed as vT
Q1) A child on a merry-go-round with a period of 3.5seconds is sitting 0.75m from the
center. What is the tangential speed of the child?
Ans) 1.35m/s
Q2) A horse races once around a circular track in a time of 118s, with a speed of 17m/s.
What is the radius of the track?
ans) 320m
Q3) The tips of the blades in a flood blender are moving with a speed of 21m/s in a circle
that has a radius of 0.053m. How much time does it take for the blades to make one
revolution?
ans) 0.016sec
► Angular Speed (=rotational speed)
 Angular speed is the number of revolutions in a given amount of time.
Angular speed =
Demo1) Tangential speed vs Angular speed
Two weights are placed on a spinning disk. Weight-A is placed farther away from the
central axis than weight-B.
A
B
Q4) Which weight has higher tangential speed?
a) Weight-A
b) Weight-B
c) The same
Q5) Which weight has higher angular speed?
a) Weight-A
b) Weight-B
c) The same
Q6) If we spin the disk faster, which weight will fly away first?
a) Weight-A
b) Weight-B
c) The same
► Angular speed(w) and Tangential speed (vT )
Angular displacement() is expressed in three units. They are degrees, revolution and
radians. The units mostly used in science is radians.
Since angular speed(w) = ∆ / ∆t, the unit for ‘w’ is rev/s or
rad/s
 (in radians) = arc length / radius = s / r
1 rad = 57.3=0.159 revs
vT = (
Q7) Convert revolutions into radians
i) 4 rev = (
) rads
ii) 0.5rev = (
)×(
)
) rads
Q8) A spinning top makes 24 rotations in 0.5 seconds. What is the angular speed in
radians?
Ans) 302rad/s
Q9) The engine of a car rotates 2000rev/min. i) How many rotation does it make in 1
second?(=angular speed). ii) Convert into radian/sec.
Ans) i)33.3rev/s ii) 210rad/s
Q10) A gymnast on a high bar swings through two revolutions in 1.9s. Find the angular
speed(in rad/s) of the gymnast.
Ans) 6.62rad/s
►Newton’s 1st Law and ‘Inertia vs Rotational Inertia’
1. Motion in a Straight Line (Linear motion)
● If you push an object, it will start moving (start increasing its speed). What is the
relation between force(F), mass(m), acceleration(a)?
acceleration = (
)
● If an object is heavy ( having a lot of mass), it will be difficult to make it move
compared to a lighter object. Furthermore, if the heavy object is already moving, it will
be more difficult to make it stop compared to a lighter object. (Newton’s 1st Law)
=> We call this property (
)
2. Rotational Motion
►Demo2) ‘Which is the better Tube to Rotate?’
There are two plastic tubes. Tube-A and tube-B. Each tubes have weights inside.
However, in tube-A, the weights are positioned at each end of the tube, and tube-B have
weights in the middle. The mass (weight) of the tubes are the same, but the mass
(weights) are distributed differently. Which tube do you think will rotate better(easier)?
a) Tube-A will rotate better!!
b)Tube-B will rotate better!!
►Torque & Rotational Inertia
- To make an object rotate, we must apply a force at a certain distance away from the axis
=> ex) pushing a door
angular acceleration = (
where, the torque ( τ) = (
)
) and the rotational inertial ( I ) = (
)
Q11) Which tube has larger rotational inertia?
a) Tube-A!
b) Tube-B!
Q12) If an object has a lot of rotational inertia, will it be easier to rotate or more
difficult? Explain!
► Demo3) ‘Balance the Tube on your Finger’
3 to 5 students should participate. The tube will have all the mass(weights) positioned
on one end while the other end has no weights. Balance the tube with your finger.
Case1: when the heavier end is on the top.
Case2: when the heavier end is on your finger. Which will be more easier to balance?
For each case, write the time it took to balance the tube
Time / Student
Student A
Student B
Student C
Case 1
Case 2
Q13) From what you observed, which case was easier to balance? Why?
►Demo4) ‘Race between a Disk and a Ring’
A disk and a ring with equal mass are on top of slope. Which will hit the bottom first?
Why?
a) The Disk!!
b)The Ring!!
► Linear Momentum vs Angular Momentum
The formula for linear momentum and Angular Momentum
Linear Momentum = (
Angular Momentum = (
)×(
)×(
)
)
► Conservation of Linear Momentum and Angular Momentum
● Conservation of Linear Momentum
If one object is standing still while another object with the same mass collides and if there
is no external force acting from outside the system, then the net momentum before the
collision and the net momentum after the collision is conserved!!
● Conservation of Angular Momentum
If no external Torque is acting on the rotating system, angular momentum of the
system does not change
Demo5) Change the Mass Distribution while Rotating
You are rotating on a spinning disk with are arms spread apart. If you pull your arms
together will you rotate faster or slower?
a) faster!
b) slower!
Q14) i) Is there an external torque acting on the system? Yes or no?
ii) Explain conservation of angular momentum using the formula ‘Iw’
Q15) A blackhole is when a star collapse inwards, which results in an enormous density.
Will the blackhole spin faster or slower than when it was a normal star?
Q16) If polar ice-caps melt and spread out throughout the Earth, will the Earth rotate
faster or slower? Why?