IGNOU PHE 1 BPHE 101 2026 - A solid cylinder rolls up an inclined plane without slipping. If the i

Question

A solid cylinder rolls up an inclined plane without slipping. If the incline makes an angle of $30^\circ$ to the horizontal and the coefficient of static friction is $\mu_s = 0.40$ , find its acceleration. Also determine the angle of the inclined plane at which the object will start to slip.

10 Feb 2026

Answer :

Word Count : 262

Let a solid cylinder of mass (m) and radius (R) roll up an inclined plane of angle (\theta) without slipping. The forces acting on it are gravity (mg), normal reaction (N), and static friction (f) acting up the incline to prevent slipping. The acceleration (a) of the center of mass and angular acceleration (\alpha) are related by the rolling condition: (a = R \alpha). Using Newton’s second law along the incline: [ mg \sin\theta - f = m a ] For rotation about the center of mass: [ f R = I

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