A catapult with a radial arm 4 m long accelerates a ball of mass 20 kg through a

Question

A catapult with a radial arm 4 m long accelerates a ball of mass 20 kg through a quarter circle. The ball leaves the apparatus @ 45m/s . If the mass of the arm is 25 kg & the acceleration is uniform , find
a. the angular acceleration
b. moment of inertia for ball & arm
c. the net torque exerted on ball & arm
hint : use the time independent rotational kinematics equation to find angular rotation - rather than the angular velocity equation -
please help - I am having problem with a. - please explain

Explanation / Answer

length of arm l = 4.00 m mass of ball m = 20 kg the ball accelerates for a quarter circle that is =(/4) radians The ball leaves the apparatus at v = 45 m/s mass of arm M = 25 kg a.   the time for which the ball accelerates is                 v = u + gt                 t = (v/g) the angular displacement is = w_0 t + (1/2) t^2                                                  = (1/2) t^2                                                   = (2/ t^2 ) substitute the above values to get solution             = .............. rad /s^2 b. the moment of inertia of the arm is                I = m * (l^2 /3) the moment of inertia of the ball is            (1/2)m * v^2 = (1/2)I * w^2               m * v2 = I * (v/r)2 = I *(v2/r2)                      I = m * r2 ---------(1) the angular speed is w = wo + t                                    w = t                                v = r * w                        r = (v/w) -----------(2)     from (1) and (2)             I = m *  (v/w)^2    substitute the values to get solution c.   the net torque exerted on the ball is = F * r = m * g * r the net torque exerted on the arm is = F * l = M * g * l            substitute the values to get saolution length of arm l = 4.00 m mass of ball m = 20 kg the ball accelerates for a quarter circle that is =(/4) radians The ball leaves the apparatus at v = 45 m/s mass of arm M = 25 kg a.   the time for which the ball accelerates is                 v = u + gt                 t = (v/g) the angular displacement is = w_0 t + (1/2) t^2                                                  = (1/2) t^2                                                   = (2/ t^2 ) substitute the above values to get solution             = .............. rad /s^2 b. the moment of inertia of the arm is                I = m * (l^2 /3) the moment of inertia of the ball is            (1/2)m * v^2 = (1/2)I * w^2               m * v2 = I * (v/r)2 = I *(v2/r2)                      I = m * r2 ---------(1) the angular speed is w = wo + t                                    w = t                                v = r * w                        r = (v/w) -----------(2)     from (1) and (2)             I = m *  (v/w)^2    substitute the values to get solution c.   the net torque exerted on the ball is = F * r = m * g * r the net torque exerted on the arm is = F * l = M * g * l            substitute the values to get saolution

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