Irodov – Problems in General Physics

Fig. 3.

1.41. R = a 3 12bs, w = all1+ (4bs 2 1a^3 )^2.
1.42. (a) w = 2av 2 , R = I/ 2 a; (b) w = bv^2 /a^2 , R = a 2 /b.
1.43. v = 2Rco = 0.40 m/s, w = 4Ro.i 2 = 0.32 m/s 2.
1.44. w= (v/t) 1/1 4a^2 t^4 = 0.7 m/s^2.
1.45. co = 231nvil = 2.0.10 3 rad/s.
1.46. (a) (cD). 2a/3 = 4 rad/s, (A) = j/ 3ab = - 6 rad/s 2 ; (b)
= 21/3ab =12 rad/s 2.
1.47. t= ir(4/a) tan a = 7 s.
1.48. (o.)) = o.) 0 /3.
1.49. (a) cp = (1 - e') coda; (b) 6.)
1.50. coz = f li213 0 sin cp, see Fig. 3.
1.51. (a) y = v 2 /(32; (hyperbola); (b) y = 1/2wx/o.)
1.52. (a) WA = v 2 /R = 2.0 m/s^2 , the
vector WA is permanently directed to the
centre of the wheel; (b) s = 8./1 = 4.0 m.
1.53. (a) vA -=---2wt =10.0 cm/s,
wt = 7.1 cm/s, vo = 0; (b)
=2w 1/1 (wt 2 /2R) 2 =5.6 cm/s 2 ,
= will+ (1-wt 2 /R) 2 ---- 2.5 cm/s 2 ,
= w 2 t 2 /R = 2.5 cm/s^2.
1.54. RA= 4r, Rg= 2 1/2-r.
1.55. co= Vo4-1- co: =5 rad/s, j3= 0)0),^2 = 12
1.56. (a) w = at 1/1 (btla) 2 =8 rad/s,
=1.3 rad/s 2 ; (b) 17°.
1.57. (a) (.6-= vIR cos a = 2.3 rad/s,
=2.3 rad/s^2.
1.58. o.)= coo yi + cootiwor 0.6 rad/s,^ (3= [30111 Oot^2 =
= 0.2 rad/s 2.
1.59. t1m = 2mwl(g^ w).
1.60. ar = (nit+ m2) , g, T - (1, ±k) m° m 2 g.
nto-rmi-rm2
'1.61. (a) (k1- k2) mi,m2g

Cosa.

m1 (b) tan a^ = kinii+ k2m2^

ms

min mi + 77 , 2 •

1.62. k = [(1 2 - 1)1(1 2 + 1)1 tan a = 0.16.

1.63. (a) m 2 /m 1 > sin a k cos a; (b) m 2 /m^1 < sin a - k cos a;

(c) sin a - k cos a <m 2 /mi < sin a k cos a.

1.64. w 2 = g (ri - sin a - k cos a)/(i + 1) = 0.05 g.

1.65. When t G to, the accelerations w 1 = w 2 = at/(m^1 + m2);

when t > to w (^1) = kgm 2 /m 1 , w 2 = (at - km 2 g)Im 2. Here to
= kgm 2 (m 1 + m 2 )1am. See Fig. 4.
1.66. tan 2a = -1/k, a = 49°; tm in = 1.0 s.
1.67. tan3= k; T = mg (sin a k cos cc)11/ 1+k^2.
= woe -at.
(parabola).
Vg=-
WA=
rad/s 2.
p = all1+ (2bt/a) 2
60°; (b) 1= (v/R)^2 tan a =
2 3 c
1.68. (a) v=
mg 2 cos a (b)
s=
m g os a
2a sin^2 a '^ 6az sina a •
1.69. v =11(2g/3a) sin a.