A solid cylinder of radius 1.3 m and mass 4.1 kg is at rest. A 4.0 N m torque is applied to the cylinder about an axis through its centre.

Question

Calculate the angular velocity of the cylinder, in rad s^-1 , after the torque has been applied for 2.0 s.

Answer 1

Given:

R = 1.3m

M = 4.1 kg

T = 4 N*m

ω_o = 0 rad/s (starts at rest)

Find:

ω after t = 2 seconds

Solution

ΣT = Iα

T = Iα

I = (1/2) * M * R^2

T = (1/2) * M * R^2 * α

α = 2*T/(M*R^2)

α = 1.15 rad/s^2

ω = αt+ω_o

∴ ω = αt = 1.15 * 2 = 2.3 rad/s^2