Question

A solid cylinder rolls down an incline plane without slipping. If the center of mass of the cylinder has a linear acceleration of 2.67 m/s2, what is the angle of the incline to the horizontal?

Answer 1

T = our unknown angle theta
angular acceleration = alpha = d omega/dt
I = (1/2) M R^2
FF = friction force up slope
FF * R = torque
so
FF * R = (1/2) M R^2 * alpha
FF = (1/2)M R alpha

R omega = no slip velocity
R alpha = no slip acceleration = a
so FF = (1/2) M a

F = m a
F = M g sin T - FF = M (2.67)

M g sin T - (1/2)M (2.67) = M(2.67)

9.81 sin T = 1.5 (2.67)

Answer 2

Thanks