Consider the rotating cylinder shown in Fig 5.26. Suppose that m= 5 kg, F = 0.60 N, and r = 0.20 m. Calculate (a) the torque acting on the cylinder, and (b) the angular acceleration of the cylinder.
(Moment of inertia of cylinder = 1212mr²
(Ans: 0.12 N, 12 rad s⁻¹)
Data Given:
m = 5.0 kg
F = 0.60 N
r = 0.20 m
θ = 90°
To Find:
(a) Torque acting on the cylinder = →T = ?
(b) Angular Acceleration = ∝ = ?
Solution:
(a) Torque acting on the cylinder = →T = ?
We know that
→T = →r x→F
or
→T = r F sin θ
By putting values
→T = 0.20 m x 0.60 N x sin 90°
→T = 0.12 N m x 1
→T = 0.12 N m -------Ans. (1)
(b) Angular Acceleration = ∝ = ?
We know that
T = I ∝
or
∝ = TI
where moment of inertia I= 12 mr², So
∝ = 2Tmr²
putting values
∝ = 2x0.12Nm5.0kgx(0.20m)²
∝ = 0.24Nm5.0kgx0.04m²
∝ = 0.24Nm0.20kgm²
∝ = 1.20 rad s⁻²}`
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