The magnitudes of the applied force F and the frictional force f of a wheel

[hidemi]

Homework Statement

A solid wheel with mass M, radius R, and rotational inertia MR^2/2, rolls without sliding on a horizontial surface. A horizontal force F is applied to the axle and the center of mass has an acceleration a. The magnitudes of the applied force F and the frictional force f of the surface, respectively, are:

a. F = Ma, f = 0
b. F = Ma, f = Ma/2
c. F = 2Ma, f = Ma
d. F = 2Ma, f = Ma/2
e. F = 3Ma/2, f = Ma/2

Ans: E

Relevant Equations

F R = (1/2 MR^2 + MR^2 ) a/R

I calculate in this way as follows and get a correct answer. Howere I am not sure if I am using the right way.

F R = (½ MR^2 + MR^2 ) a/R
F = 3/2 Ma
F - f = Ma
f = 3/2 Ma - Ma = Ma/2

 

[haruspex]

Homework Statement:: A solid wheel with mass M, radius R, and rotational inertia MR^2/2, rolls without sliding on a horizontial surface. A horizontal force F is applied to the axle and the center of mass has an acceleration a. The magnitudes of the applied force F and the frictional force f of the surface, respectively, are:

a. F = Ma, f = 0
b. F = Ma, f = Ma/2
c. F = 2Ma, f = Ma
d. F = 2Ma, f = Ma/2
e. F = 3Ma/2, f = Ma/2

Ans: E
Relevant Equations:: F R = (1/2 MR^2 + MR^2 ) a/R

I calculate in this way as follows and get a correct answer. Howere I am not sure if I am using the right way.

F R = (½ MR^2 + MR^2 ) a/R
F = 3/2 Ma
F - f = Ma
f = 3/2 Ma - Ma = Ma/2

The safest way with angular acceleration is to take moments about either the mass centre or a fixed point.
You have effectively taken the second option.

 

[hidemi]

The safest way with angular acceleration is to take moments about either the mass centre or a fixed point.
You have effectively taken the second option.

Thanks for commenting.