A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N ? What is the linear acceleration of the rope ? Assume that there is no slipping.
Solution and Explanation
Mass of the hollow cylinder, m = 3 kg
Radius of the hollow cylinder, r = 40 cm = 0.4 m
Applied force, F = 30 N
The moment of inertia of the hollow cylinder about its geometric axis: I = mr 2
= 3 × (0.4)2 = 0.48 kg m2
Torque, π = F × r
= 30 × 0.4 = 12 Nm
For angular acceleration , torque is also given by the relation : π = Ia
α =\(\frac{ π }{ I} = \frac{12 }{ 0.48}\)
= 25 rad s -2
Linear acceleration = rα = 0.4 × 25 = 10 m s-2
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Concepts Used:
Torque
Torque is a moment of force. Torque is measured as a force that causeque is also defined as the turning effect of force on the axis of rotation. Torque is chs an object to rotate about an axis and is responsible for the angular acceleration. Characterized with “T”.
How is Torque Calculated?
Torque is calculated as the magnitude of the torque vector T for a torque produced by a given force F
T = F. Sin (θ)
Where,
r - length of the moment arm,
θ - the angle between the force vector and the moment arm.
Read More: Torque
Types of Torque
Torque is of two types:
- Static torque
- Dynamic torque