Download PHY 1114: Physics I Practice Problem Think about it

Practice Problem
PHY 1114: Physics I
• The diameter of your tires is 0.60 m. You make a 60
mile trip at a speed of 45 mph.
Lecture 11:
(a) During this trip, what was your tires’ angular
Rotational MotioN
speed? Recall 1 mph = 0.447 m/s
(b) How many times did they revolve?
Fall 2012 Kenny L. Tapp
Think about it...
Rigid Bodies, Translations, & Rotations
A ball on the end of a string swings in a horizontal circle once
every second. State whether the magnitude of each of the
following quantities is zero, constant (but not zero), or changing:
a. Velocity
d. Angular Acceleration
b. Angular Velocity
e. Tangential Acceleration
A rigid body, in which distances between particles are fixed, may have translational
motion, rotational motion, or a combination. It may roll with or without slipping.
Every point
on a rotating
rigid body
has the same
angular
velocity ω!
c. Centripetal Acceleration
Rotational Forces
Rotational Forces
Consider pushing open a heavy door. Four forces are shown, all
of equal strength. Which of these will be most effective at
opening the door?
The ability of a force to cause a rotation is dependent
upon 3 factors:
1. The magnitude F of the force
F1
Hinge
F3
Far Side Cartoon by Gary Larsen
F4
F2
2. The distance r from the axis which an object can rotate,
to the point where the force F is applied
3. The angle at which the force F is applied
Torque, Equilibrium, & Stability
It takes a force to start an object rotating; that force is more
effective the farther it is from the axis of rotation, and the closer it
is to being perpendicular to the line to that axis.
Quick Question 1
• In trying to open a stuck classroom door, Prof. Tapp
pushes it at a point 0.8 m from the hinges with a 220 N
force that is directed 20° away from being
perpendicular to the door. What torque does Tapp exert
on the door?
Torque, Equilibrium, & Stability
The perpendicular distance from the line of force to the axis of
rotation is called the lever arm.
The product of the force and the lever arm is called the torque.
Quick Question 2
• The bolts on a car wheel require tightening to a torque
specification of 90 mN. If a 0.20 m long wrench is
used, what is the magnitude of the force required:
(a) when the force is perpendicular to the length of
the wrench?
(b) when the force is at θ = 35° to the length of the
wrench?
Torque, Equilibrium, & Stability
In order for an object to be in
equilibrium, the net force on it must be
zero, and the net torque on it must be
zero as well.
Rotational Dynamics
The net torque on an object causes its angular acceleration. For a
point particle, the relationship between the torque, the force, and
the angular acceleration is relatively simple.
Recall at = rα and at = F/m.....we can
rewrite and combine into one equation: α = F/(mr)
Recall 𝜏 = rF, thus F = 𝜏/r.....with this
relationship, we can rewrite our equation for α:
α = 𝜏/(mr2)
We now have an equation that gives a relationship between torque on a
single particle and its angular acceleration.
Rotational Dynamics
Moments of Inertia
We can consider an extended object to be a lot of near-point
objects (single particles) stuck together. Then the net torque is:
Net torque is the
cause of angular
acceleration.
The quantity inside the parentheses is called the object’s
moment of inertia, I.
Moment of inertia is
the rotational
equivalent of mass.
Net torque is the
cause of angular
acceleration.
Net torque is
cause of angu
acceleration
Quick Question 3
Moments of Inertia
• The engine in a small airplane is specified to have a torque of 500
Nm. This engine drives a 2.0 m-long, 40 kg single-blade propeller.
On start-up, how long does it take the propeller to reach 2000 rpm?
ebay.com
This is a rod rotating about its center
Solve for
α
Solve for
I
Solve for time
knowing ∆ω
Net torque is the
cause of angular
acceleration.
Quick Question 4
Quick Question 4
• A 5.0 m tall telephone pole with
a mass of 260 kg had just been
hit by a tornado, mostly
severing the pole at its base.
The pole falls, rotating about the
part still connected to the base.
Estimate the pole’s angular
acceleration when it has fallen
25° from the vertical.
A falling telephone pole undergoes an angular
acceleration due to a gravitational torque.
The pole’s weight w is acting at the center of gravity. The torque
on the pole is thus due only to the gravity and is rotating the pole
in a counterclockwise direction, so the torque is positive.
Note: Fg = w⊥= w sinθ = mg sinθ
w⊥
L/2
θ=25°
𝜏 = r F = (L/2) Fg = (L/2) w sinθ
w
Note: Model the pole as a uniform rod rotating about one end.
Tornado damage in Norman, OK from April 13, 2012
𝜏 = (mgL/2) sinθ
α = 𝜏/I
Quick Question 5
• A standing athlete lifts a barbell by
moving on his forearms, which pivot at
the elbow. The weight lifted in the curl
is over 200 pounds (about 900 N). The
distance from the tendon to the elbow
joint is 4.0 cm and from the barbell to
the elbow is 35 cm.
Quick Question 5
For the forearm to be in static equilibrium, the net force and
net torque on it must both be zero.
Ft
Lifting muscle
(biceps)
∑Fy = Ft - Fe - Fb = 0
Tendon
4 cm
35 cm
a. What is the tension in the tendon connecting the biceps muscle to the bone while a 900 N
barbell is held stationary in this position?
b. What is the force exerted by the elbow on the forearm bones?
Recall 𝜏 = r F...
𝜏net = [Ft rt] - [Fe re] - [Fb rb] = 0
re = 0 cm
Fe
Fb
rt = 4 cm
rb = 35 cm