Question

ZOOM 40.0 cm, and mass m = 600 kg 2. A solid cylinder has length L = 50.0 cm, radius R Starting from rest, it is uniformly accelerated for 5.0 seconds, until spinning around its axis at 20 rev/s a. What is the angular acceleration in rad/s2? b. Through what angular displacement did the cylinder turn in these 5.0 s?

A solid cylinder has length L = 50.0 cm, radius R = 40.0 cm, and mass m = 600 kg. Starting from rest, it is uniformly accelerated for 5.0 seconds, until spinning around its axis at 20 rev/s.

a. What is the angular acceleration in rad/s2 ?

b. Through what angular displacement did the cylinder turn in these 5.0 s?

Answer 1

a) Moment of inertia of a cylinder about its axis = Mr^2 / 2

= 600*0.4^2 / 2 = 48 kg-m^2

angular speed = 2pi*N = 2pi*20 = 125.66 rad/s

using the equation of angular motion we have

w = wo + $\alpha$t

125.66 = 0 + $\alpha$*5

$\alpha$ = 25.13 rad/s^2

b) w^2 = wo^2 + 2$\alpha$$\theta$

125.66^2 = 0 + 2*25.13*$\theta$

$\theta$ = 314 rad

= 314/2pi = 50 revolutions