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Power; Rotational Energy

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- Power
- Rotational work, power, and kinetic energy.

Serway & Jewett 7.5, 10.4, 10.8

Physics 1D03 - Lecture 21

Physics 1D03 - Lecture 21

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

f

F

r

ds = rdq

d

Rotational Work

A bit of work, dW, is done in turning a nut through a tiny angle d :

So,

and so for a constant torque,

Physics 1D03 - Lecture 21

Power:

So,

(again, angular velocity must be expressed in radians/second).

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

- 60W
- 6 W
- 1 W

Physics 1D03 - Lecture 21

vi

w

but

so

K = ½ Iw 2

Kinetic energy of a rotating rigid body:

Add up the kinetic energies of the particles:

Physics 1D03 - Lecture 21

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

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

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?

- 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

- 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 21.(5th ed):
- Chapter 7, problems 37, 47a
- Chapter 10, problems 23.

Physics 1D03 - Lecture 21