Username: Arvind BordeBook: Physics: Principles with Applications, Seventh Edition. No part of any book may be reproduced or transmitted in any form by any means without the publisher's prior written permission. Use (other than pursuant to the qualified fair use privilege) in violation of the law or these Terms of Service is prohibited. Violators will be prosecuted to the full extent of the law.

Username: Arvind BordeBook: Physics: Principles with Applications, Seventh Edition. No part of any book may be reproduced or transmitted in any form by any means without the publisher's prior written permission. Use (other than pursuant to the qualified fair use privilege) in violation of the law or these Terms of Service is prohibited. Violators will be prosecuted to the full extent of the law.

off by 6piper rev

a) Rb) R & Tc) T

Yes, big r

Less torqueneeded

Spread out(bigger I)

Friction

2054903 2015/11/09 24.90.60.53

Username: Arvind BordeBook: Physics: Principles with Applications, Seventh Edition. No part of any book may be reproduced or transmitted in any form by any means without the publisher's prior written permission. Use (other than pursuant to the qualified fair use privilege) in violation of the law or these Terms of Service is prohibited. Violators will be prosecuted to the full extent of the law.

Username: Arvind BordeBook: Physics: Principles with Applications, Seventh Edition. No part of any book may be reproduced or transmitted in any form by any means without the publisher's prior written permission. Use (other than pursuant to the qualified fair use privilege) in violation of the law or these Terms of Service is prohibited. Violators will be prosecuted to the full extent of the law.

Username: Arvind BordeBook: Physics: Principles with Applications, Seventh Edition. No part of any book may be reproduced or transmitted in any form by any means without the publisher's prior written permission. Use (other than pursuant to the qualified fair use privilege) in violation of the law or these Terms of Service is prohibited. Violators will be prosecuted to the full extent of the law.

2054903 2015/11/09 24.90.60.53

Username: Arvind BordeBook: Physics: Principles with Applications, Seventh Edition. No part of any book may be reproduced or transmitted in any form by any means without the publisher's prior written permission. Use (other than pursuant to the qualified fair use privilege) in violation of the law or these Terms of Service is prohibited. Violators will be prosecuted to the full extent of the law.

Username: Arvind BordeBook: Physics: Principles with Applications, Seventh Edition. No part of any book may be reproduced or transmitted in any form by any means without the publisher's prior written permission. Use (other than pursuant to the qualified fair use privilege) in violation of the law or these Terms of Service is prohibited. Violators will be prosecuted to the full extent of the law.

15 kg m/s6 N m

Homework 8 hints

A few reminders:

Kinematical linear quantities are often related to their rotational

counterparts through multiplication by the radius:

Displacement: d = r✓

Speed/velocity: v = r!

Acceleration: aT = r↵

In each case the same word is used in the rotational world with

a “rotational” tagged onto the linear word. If a new word is

needed, it is explicitly written down below.

The relationship of dynamical linear quantities to their rotational

counterparts is not always so simple, but here’s a list of the two

sets:

Inertia: m, I

Force/torque: F, ⌧

Momentum: p, L

Within the rotational world the interrelationship of rotational

quantities parallels that of linear quantities:

p = mv: L = I!

F = ma: ⌧ = I↵

F = �p/�t: ⌧ = �L/�t

KE =12mv2: KErot =

12I!

2

W = Fd: W = ⌧✓

Keeping these in mind allows you to answer the questions and

misconceptuals.

Hints for problems (pages 222–225):

2.Use d = r✓, converting ✓ to radians; r is the given earth-sun

distance, and d will be the diameter of the sun.

3.Use d = r✓ where ✓ is the given angle and r the given earth-

moon distance.

11.The earth spins through 2⇡ radians in 24 hours. Calculate

the angular speed, !, in radians/second. Using RE = 6.4⇥106m,

and v = r! you can directly get the linear speed at the equator.

For another latitude, ⇥, the e↵ective radius you use is RE cos⇥.

14.Do this in steps: (i) convert rpm to radians per second to get

!i and !f . (ii) Given these two and the time, use the appropriate

equation to get ↵. (iii) ↵ allows you to get aT , after you convert

the given r to m. (iv) Use your new knowledge of ↵ to get ! at

the 2 sec mark, and use that ! and r to get v. (v) Use v and rand the formula for centripetal acceleration to get aR.

17.Do this in steps: (i) convert rpm to radians per second to get

!i and !f . (ii) Given these two and the time, use the appropriate

equation to get ↵. (iii) Get the total angle by using any equation

that has theta in it, then get number of revolutions from it.

18.Similar steps to previous.

24.Force exerted by cyclist is mg. Get torque from the force and

the radius.

26.Use equation giving torque from force, r and ✓.

50.Use formula for rotational KE.

60.Calculate I, the moment of inertia, from m and r. Once you

have it, calculate L, the angular momentum.

61.Page 210 lists the moments of inertia for di↵erent objects.

Use that and ! (from rpm information) to get L. Use change in

L and t to get the torque.

1. (a) 0.785398,⇡/4. (b) 1.0472,⇡/3. (c) 1.5708,⇡/2. (d) 6.28319, 2⇡. (e) 7.76672, 89⇡/362. 0.5� ! 0.00872665 rad.. Diameter is d = r✓ = (150⇥ 10

6)(0.00872665) = 1.31⇥ 10

6km. So radius is 6.5⇥ 10

5km.

3. Diameter is d = r✓ = (3.8⇥ 105)(1.4⇥ 10

�5) = 5.3 km.

11. Earth’s angular speed is ! = 2⇡/(24 ·3600) = 0.000073 rad/s. Linear velocity at equator is RE! = 467.2m/s. At 66.5�, the speedis is RE! cos 66.5� = 186.3m/s. At 42

�the speed is RE! cos 42

�= 347.2m/s.

14. (i) !i = (120 ⇥ 2⇡)/60 = 12.6 rad/s. !f = 29.3 rad/s. (ii) !f = !i + ↵t, so 29.3 = 12.6 + 4↵. Or ↵ = 4.2 rad/s2. (iii) aT =

r↵ = (0.305)(4.2) = 1.3m/s2. (iv) ! = 12.6 + (4.2)(2) = 21 rad/s. v = r! = (0.305)(21) = 6.4m/s. (v) aR = v2/r = (6.4)2/0.305 =

134.3m/s2.

17. (i) !i = (3500 ⇥ 2⇡)/60 = 366.5 rad/s. !f = 125.7 rad/s. (ii) !f = !i + ↵t, so 125.7 = 366.5 + 2.5↵. Or ↵ = �96.3 rad/s2.(iii) !2

f = !2i + 2↵✓. So, ✓ = 615.2 rad, or 97.9 revs.

18. (i) !i = 0 rad/s. !f = 1570.8 rad/s. (ii) !f = !i + ↵t, so 1570.8 = 240↵. Or ↵ = 6.5 rad/s2. (iii) !2f = !2

i + 2↵✓. So,

✓ = 188,496 rad, or 30,000 revs.

26. ⌧ = rF = (0.17)(52)(9.8) = 86.6N·m. She can exert more torque by using longer pedals or by gaining weight.

28. (a) ⌧ = rF = (0.96)(42) = 40.3N·m. (b) ⌧ = rF = (0.96)(42) sin 60� = 34.9N·m.

50. ! = (8750⇥ 2⇡)/60 = 916.3 rad/s. KE =12I!

2=

12 (3.25⇥ 10

�2)(916.3)2 = 13,643.6 J.

60. I = mr2 = (0.270)(1.35)2 = 0.49 kg·m2. L = I! = (0.49)(10.4) = 5.1 kg·m2

/s.