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Physics 1D03 - Lecture 21
Power; Rotational Energy
• Power• Rotational work, power, and kinetic energy.
Serway & Jewett 7.5, 10.4, 10.8
Physics 1D03 - Lecture 21
Recall:
rs rvt
rat
iif t
222
22
1
if
iif tt
Physics 1D03 - Lecture 21
Power
Power is the rate at which work is done:
Average power = Work/time
Instantaneous power: Average over an infinitesimal time dt, displacement ds; the work is dW = F • ds, and power is
units: 1 J/s =1 watt (W)
vFds
F dtdt
dWP
Physics 1D03 - Lecture 21
Rotational Work
A bit of work, dW, is done in turning a nut through a tiny angle d :
d
drF
dsF
dW
)sin(
)sin(
dsF
rF
ds = rd
d ddW
W
So,
and so for a constant torque,
Physics 1D03 - Lecture 21
Power:
dtd
dtd
dtdW
P ) (
(again, angular velocity must be expressed in radians/second).
PSo,
Physics 1D03 - Lecture 21
Quiz
A power screwdriver is intended to provide a torque of 0.5 N·m while turning at 120 revolutions per minute. The minimum power needed from the motor will be about
A) 60WB) 6 WC) 1 W
Physics 1D03 - Lecture 21
Kinetic energy of a rotating rigid body:
Add up the kinetic energies of the particles:
221
iiii
i vmKK
ii rv but
22122
21 IrmK i
ii
so
vi
K = ½ I 2
Physics 1D03 - Lecture 21
A wheel is spun up to speed by a motor that produces a constant power. It takes time t to reach an angular velocity . Assuming negligible friction at the axle, how long does it take to reach twice this angular velocity?
t
t
2 d)
2t c)
22 b)
4t a)
Quiz
Physics 1D03 - Lecture 21
a) How much kinetic energy do they have at 7200 rpm?
b) How long does a 7-watt motor take to get the drive up to speed?
Example
A computer hard drive has four 100-gram platters (disks), 10 cm in diameter. (Uniform thin disk: I= ½ M R2)
Physics 1D03 - Lecture 21
Example: Big Ben, a tower clock in London has an hour hand 2.7m long with a mass of 60kg and a minute hand 4.5m long with a mass of 100kg. Calculate the rotational kinetic energy of the two hands.
(I=1/3 ML2)
Big Ben
Physics 1D03 - Lecture 21
Quiz
A cone-shaped top is launched by winding a string of length L around the top, and pulling with a constant force F. How should the string be wound to do the greatest amount of work on the top?
a) wind it around the thick end
b) wind it around the thin end
c) it doesn’t matter how it is wound
d) not enough information
F
Physics 1D03 - Lecture 21
Summary
Suggested Problems:
Chapter 7, problems 35, 40a (5910W)Chapter 10, problems 21.
(5th ed):Chapter 7, problems 37, 47aChapter 10, problems 23.
• Power: P=dW/dt = F • v
• Rotation: dW = d P = K = ½ I2
