A string is wrapped around a uniform solid cylinder of radius r, as shown in (Figure 1).

Question

A string is wrapped around a uniform solid cylinder of radius r. as shown in Figure 1. The cylinder can rotate freely about its axis, The loose end of the string is attached to a block. The block and cylinder each have mass m. Find the magnitude an of the angular acceleration of the cylinder as the block descends.

Express your answer in terms of the cylinder’s radius r and the magnitude of the acceleration due to gravity g.

Give T a chance to be the string strain (Tension). That the precise quickening (angular acceleration) alpha are the questions. Separate conditions for the speeding up of the square and the rakish (angular acceleration speed) increasing speed of the chamber will enable you to settle for the two factors. The snapshot of dormancy of the chamber in (1/2) M r^2
m g – T = m a
T*r = torque = I*alpha = (1/2) m r^2 * alpha
T = (1/2) m*r*alpha
m g = mama + (1/2) m r * alpha
= mama + (1/2) m a
(since alpha = a/r)
a = (2/3) g
alpha = (2/3)(g/r)alpha = (2/3)(g/r)

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Answer ( 1 )

  1. Give T a chance to be the string strain (Tension). That the precise quickening (angular acceleration) alpha are the questions. Separate conditions for the speeding up of the square and the rakish (angular acceleration speed) increasing speed of the chamber will enable you to settle for the two factors. The snapshot of dormancy of the chamber in (1/2) M r^2
    m g – T = m a
    T*r = torque = I*alpha = (1/2) m r^2 * alpha
    T = (1/2) m*r*alpha
    m g = mama + (1/2) m r * alpha
    = mama + (1/2) m a
    (since alpha = a/r)
    a = (2/3) g
    alpha = (2/3)(g/r)alpha = (2/3)(g/r)

    Best answer

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