1. Power; Rotational Energy
Rotational work, power, and kinetic energy.
Serway & Jewett 7.5, 10.4, 10.8
Physics 1D03 - Lecture 21

2. Recall:
Physics 1D03 - Lecture 21

3. Power Average power = Work/time
Power is the rate at which work is done:
Average power = Work/time
units: 1 J/s =1 watt (W)
Instantaneous power: Average over an infinitesimal time dt, displacement ds; the work is dW = F • ds, and power is
Physics 1D03 - Lecture 21

4. Rotational Work f F r ds = rdq So, d and so for a constant torque,
A bit of work, dW, is done in turning a nut through a tiny angle d : f r F
ds = rdq d
So,
and so for a constant torque,
Physics 1D03 - Lecture 21

5. (again, angular velocity must be expressed in radians/second).
Power:
So,
(again, angular velocity must be expressed in radians/second).
Physics 1D03 - Lecture 21

6. 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
60W
6 W
1 W
Physics 1D03 - Lecture 21

7. K = ½ Iw 2 Kinetic energy of a rotating rigid body:
Add up the kinetic energies of the particles:  vi w
but so
K = ½ Iw 2
Physics 1D03 - Lecture 21

8. Quiz
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?
Physics 1D03 - Lecture 21

9. Example
A computer hard drive has four 100-gram platters (disks), 10 cm in diameter (Uniform thin disk: I= ½ M R2)
How much kinetic energy do they have at 7200 rpm?
How long does a 7-watt motor take to get the drive up to speed?
Physics 1D03 - Lecture 21

10. Example: Big Ben, a tower clock in London has an hour hand 2
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

11. 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?
wind it around the thick end
wind it around the thin end
it doesn’t matter how it is wound
not enough information F
Physics 1D03 - Lecture 21

12. Summary Power: P=dW/dt = F • v
Rotation: dW = t dq, P = t w, K = ½ Iw 2
Suggested Problems: Chapter 7, problems 35, 40a (5910W)
Chapter 10, problems (5th ed):
Chapter 7, problems 37, 47a
Chapter 10, problems 23.
Physics 1D03 - Lecture 21