What is the angular acceleration and linear acceleration?

A rope of negligible mass is wound around 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.

Expert Solution

Mass of the hollow cylinder, m = 3 kg

Radius of the hollow cylinder, r = 40cm = 0.4 m

Force applied, F = 30 N

Moment of inertia of the hollow cylinder about its axis:

I = mr2

= 3 × (0.4)2 = 0.48 kg m2

Torque, T = F × r = 30 × 0.4 = 12 Nm

Also, we know that :

Torque = moment of inertia x acceleration

T = Iα

( a ) Therefore, α = T / I = 12 / 0.48 = 25 rad s-2

( b ) Linear acceleration = Rα = 0.4 × 25 = 10 m s–2

Angular acceleration is \( 25 rad/s^{2} \) and linear acceleration is \( 10 m/s^{2} \)

Ajay Kumar Gupta answered 3 years ago

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