Question

A sphere with mass m = 10kg and R =0.5m begins at rest and accelerates uniformly for t = 20s to a final angular speed of w = 40rev/sec. it rotates about an axis through its center
a. what is the angular acc of sphere at t=20s
b angular acc of sphere at t = 10s
c. angular displacement at t = 20s
d. moment of inertia of the sphere
e. change in rotational energy from 0 to 20s
f. tangential component of the acc at a point R/2 from the axis of rotation at t = 10s
g. radial component of the acc at point R/2 from axis of rotation when sphere has accelerated half its final angular speed
h. final speed of the equator at t=20s
total distance at a point at the equator travels during 20s

Answer 1

wf = wi + alpha t

wf = 40 x 2pi rad /s = 251.3 rad/s

251.3 = 0 + 20 alpha

alpha = 12.5 rad/s^2 .....Ans

(B) alpha is constant throughout.

alpha = 12.5 rad/s^2

(C) theta = wi t + alpha t^2 / 2

theta = 0 + (12.5)(20^2)/2

= 2513 rad

(D) I = 2 M R^2 / 5 = 1 kg m^2

(E) change in KE = I w^2 /2 = (1)(251.3^2)/2

= 3.16 x 10^4 J

(F) a_t = alpha r = (12.6) (0.5/2)

a_t = 3.15 m/s^2

(G) a_r = w^2 r = (20 x 2 pi )^2 (0.5/2)

a_r = 3950 m/s^2

(h) w = 251.3 rad/s

d = theta * r = 1256 m