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1.A small 650-gram ball on the end of a thin, light rod is rotated in a horizontal circle of radius 1.2m. Calculate
(a) The moment of inertia of the ball about the center of the circle, and
(b) The torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.
2.A metal sign for a car dealership is a thin, uniform right triangle with base length b and height h. The sign has mass M.
(a) What is the moment of inertia of the sign for rotation about the side of length h?
(b) If M = 5.40 kg, b = 1.60 m, and h = 1.20 m, what is the kinetic energy of the sign when it is rotating about an axis along the 1.20-m side at 2.00 rev/s?
3.A small ball with mass 1.30 kg is mounted on one end of a rod 0.780 m long and of negligible mass. The system rotates in a horizontal circle about the other end of the rod at 5010 rev/min.
(a) Calculate the rotational inertia of the system about the axis of rotation.
(b) There is an air drag of 2.30 x 10-2 N on the ball, directed opposite its motion. What torque must be applied to the system to keep it rotating at constant speed?
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4.A small ball of mass 0.75 kg is attached to one end of a 1.25-m-long massless rod, and the other end of the rod is hung from a pivot. When the resulting pendulum is 30° from the vertical, what is the magnitude of the gravitational torque calculated about the pivot?
5.To form a pendulum, a 0.092 kg ball is attached to one end of a rod of length 0.62 m and negligible mass, and the other end of the rod is mounted on a pivot. The rod is rotated until it is straight up, and then it is released from rest so that it swings down around the pivot. When the ball reaches its lowest point, what are?
(a) Its speed and
(b) The tension in the rod? Next, the rod is rotated until it is horizontal, and then it is again released from rest.
(c) At what angle from the vertical does the tension in the rod equal the weight of the ball?
(d) If the mass of the ball is increased, does the answer to
(c) Increase, decrease, or remain the same?
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