A An amusement park builds a ride in which the victim is mad

A) An amusement park builds a ride in which the victim is made to spin about a pole with a rocket strapped on his seat. The rider, box and rocket have an initial total mass of 230 kg. Neglect the mass of the rod of length 6 m What is the moment of inertia of rider, box and rocket about the pole? The acceleration of gravity is 9.8 m/s 2 . Treat the rider, box and rocket as a point mass. Answer in units of kg · m^2 B)The rocket develops a thrust of 64 N perpendicular to the path of the rider. What is the initial angular acceleration of the rider? Answer in units of rad/s^2 D)After what time t is the rider’s velocity equal to 6 m/s? Neglect the change in mass of the rocket. Answer in units of s.

Solution

I = M l² = 230 * 6²

I = 8280 kg.m²

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torque = l F = I alpha

alpha = l F / I = 6 * 64 / 8280

alpha = 0.046 rad/s²

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w = alpha t

v = l w = l * alpha t

t = v / l alpha = 6 / (6 * 0.046)

t = 21.74 s