disk with string urgent help

Question

A solid uniform disk of mass M = 9.8 kg and radius R = 22 cm rests with its flat surface on a frictionless table (i.e., the axis of the cylinder is perpendicular to the table.) The diagram shows a top view. A string is wrapped around the rim of the disk and a constant force of F = 11.2 N is applied to the string. The string does not slip on the rim.

1) What is the acceleration of the center of mass?

2) What is the angular acceleration about the center of mass?

3)The next 5 questions refer to a time 1.2 seconds after the force is first applied. How far has the disk moved?

4) Through what angle has the disk turned?

5) What is the translational speed of the center of mass of disk?

6) What is the angular velocity about the center of the disk?

7) What is the total kinetic energy of the disk?

Answer 1

1) Sum torque about center G

F * R = I*α

α = F*R/I

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

α = F*R/I = 2*F/M = 2.285 rad/s^2

a = α *R = 0.502 m/s^2

2) α = 2.285 rad/s^2

3) X = (1/2)*a*t^2 = (1/2) * (0.502)*(1.2)^2 = 0.361 m

4) θ = (1/2) * α * t^2 = 1.64 rad

5) V = a*t = 0.502 * 1.2 = 0.6024 m/s

6) ω = α * t = 2.285 * 1.2 = 2.742 rad/s

7) KE = (1/2)*M*V^2 + (1/2)*I*ω^2

M = 9.8 kg

V = 0.6024 m/s

I = 1/2*M*R^2 = 0.23716 Kg * m^2

ω = 2.742 rad/s

KE = 2.669 J