physics 218: lecture 14
TRANSCRIPT
Physics 218 Fall 2010 Slide 1
Physics 218: Lecture 14
Chapter 8: Rotational Motion
Torque and Newton’s Law Moment of inertia
Physics 218 Fall 2010
Physics 218 Fall 2010
Supposing two people of equal strength grab onto either side of this tire and pull. What would the free body diagram look like? What could you say about the motion of the object?
Physics 218 Fall 2010
mF
a
Supposing two people of equal strength grab onto either side of this tire and pull. What would the free body diagram look like? What could you say about the motion of the object?
0
0No acceleration => constant velocity
Physics 218 Fall 2010
Supposing two people of equal strength grab onto either side of this tire and pull this way. What would the free body diagram look like? What could you say about the motion of the object?
Physics 218 Fall 2010
mF
a
Actually the same free body diagram applies …
0
0 No acceleration => constant velocity
… for the center of mass
Physics 218 Fall 2010
The thing that is different is that there is now a torque that produces rotation about a pivot point. Torque and rotational motion are the topics this week.
Physics 218 Fall 2010
Physics 218 Fall 2010
We’ll need to describe the rotation of objects
The whole object rotates as one, so it is sufficient to know the axis of rotation and the angle,
Physics 218 Fall 2010
This is equivalent to the way we have described linear motion up to now
x
x
And, if you understand linear motion, there is a rich set of analogies to exploit
Physics 218 Fall 2010
x
Linear motion Rotational motion
position x
tva
acceleration
velocity txv
amF
angle
t
angular
acceleration
angularvelocity t
I
Physics 218 Fall 2010
Quiz
An object experiences zero net torque. Which of the following statements is true?
Hint: zero net torque is analogous to zero net force.
A.The object is not rotating.B.The object is rotating.C.The object has zero angular velocity. D.The object has constant angular velocity.E. All statements are false, including this one.
Physics 218 Fall 2010
Relationship between rotation and linear motion
In rotational motion, all points travel on a circle around the axis of rotation.
Physics 218 Fall 2010
Relationship between rotation and linear motion
rs s distance traveled
around arc
r radial distance to center of rotation
angle in radians
s
Physics 218 Fall 2010 15
Demo 1Q-1: Rotational Motion
Same angular distance.
rs
Physics 218 Fall 2010
(rad)
180
(degrees)
Convert 60 degrees from degrees to radians :
0472.13
60180
radian
Physics 218 Fall 2010
distance along arc
rs
raacceleration
velocity rv
Rotational motion
tv
angle
angularvelocity
angularacceleration
t
Basically, to get the linear quantity, take the angular quantity (in radians) and multiply by r.
Linear motion
s
Physics 218 Fall 2010
Quiz
A wind turbine spins at 22 rpm (rotations per minute). The blades are 20 m long. What is the linear speed at
the tip of the blade?
A. 1.1 m/sB. 7.3 m/sC. 77 m/sD. 46.1 m/s
Physics 218 Fall 2010 19
Quiz - CD PlayersLinear speed of the disk where the laser shines must be
maintained at a constant value of 1.25 m/s.
Does the disc spin faster when it is reading the inner or outer tracks on the disc?
A. Inner
B. Outer
Physics 218 Fall 2010 20
Quiz
Image from www.jackiechankids.com/ files/ATW.htm
R4R
Is the linear velocity at the very top of the rear wheel:
A. greater thanB. equalC. less than
the linear velocity at the top of the front wheel?
FrontWheel
RearWheel
Physics 218 Fall 2010 21
TorqueTorque, , is the rotational analog to Force.
F ma ITorque, , involves a force, F
The ability of a force to rotate an object depends on not only the magnitude of the force, but also depends on
-where the force is applied
-the direction in which the force is applied.
rF
Physics 218 Fall 2010 22
Torque
The ability of a force to rotate an object depends on not only the magnitude of the force, but also depends on
-where the force is applied
-the direction in which the force is applied.
Physics 218 Fall 2010 23
Torque
Forces along the radial direction produce no torque..
The component prependicular to r produces torque.
rF
sinFF
Physics 218 Fall 2010 24
Newton’s Second Law
F ma I
The moment of inertia, I, appears as a rotational mass.