Question

derive an expression for the 59. ** angular acceleration of the pulley of moment of inertia I in Figure 8-62. Assume the friction between the pulley and its axle are negligible. Also assume that the friction between the masses and the surfaces is negligible. m2 Either Conservation of energy or Newton's Second Law. mi Since a is being asked for, (and not w) perhaps easier to use Newton's 2nd law approach.

Answer 1

Q K mov - > Consider the free-bo diagram of the System Mat a> acceleration I 1 of m, and me d angular acceleration 1 of pulley - mg cosa I migsin T., Tz tension in the strings on the night and left of the pulley. m, do not move normal to the incline, the net force in this direction must be zero - Ne - mag=0 The equation of motion of m, in the horizontal direction is - T2 = m_a o me do not move noonal to the incline Ni migcosa=0 Equation of motion of me along the incline is - migsing -T, = mia > Ti = migising - mia -

Let R be the radius of the pulley, the free-body diagram of the pulley is showny Id= TR-T₂ R Using @ and € I N IQ = (migsinə -ma) R - MAR " Ida mi ar tm, a R = mig sina R Using a=QR Cassaming the sting does not 1 slip over the pulky) Id + m, R²a tm, R² a = migsinar al It miR²+ m_R2) = migh sind a= mig? sin I I + miR? + MARS