First slide

Rolling motion

Question

A homogeneous cylinder of mass M and radius R is pulled on a horizontal plane by a horizontal force F acting through its centre of mass. Assuming rolling without slipping the angular acceleration of the cylinder is

Moderate

A

3F / 2MR
B

2F / 3MR
C

F / 2MR
D

3F / 4MR

Solution

Torque about COM = f R
.: From
$\large \tau = I_c.\alpha$
We can write , f R = (1/2 m R²) α
f = 1/2 m R $α$ ------- (1)
From F_net = m a_c ,
F -f = m a_c ---------------- (2)
Also, a_c = R α ---------------- (3)
Solving, α = 2F / 3m R

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