Exam 11: Rotational Dynamics and Static Equilibrium

In a certain cyclotron,a proton of mass 1.67 × 10^-27 kg moves in a circle of diameter 1.6 m with an angular speed of 2.0 × 10⁶ rad/s.What is the angular momentum of the proton?

A uniform rod is 2.0 m long.It is hinged to a wall at its left end,and held in a horizontal position at its right end by a vertical very light string,as shown in the figure.What is the angular acceleration of the rod at the moment after the string is released if there is no friction in the hinge?

When is the angular momentum of a system constant?

A spinning ice skater on extremely smooth ice is able to control the rate at which she rotates by pulling in her arms.Which of the following statements are true about the skater during this process? (There could be more than one correct choice. )

An irregularly shaped object that is 10 m long is placed with each end on a scale.If the scale on the right reads While the scale on the left reads How far from the left end is the center of gravity of this object?

A light-weight potter's wheel,having a moment of inertia of Is spinning freely at 40.0 rpm.The potter drops a small but dense lump of clay onto the wheel,where it sticks a distance 1.2 m from the rotational axis.If the subsequent angular speed of the wheel and clay is 32 rpm,what is the mass of the clay?

A man in a gym is holding an 8.0-kg weight at arm's length,a distance of 0.55 m from his shoulder joint.What is the torque about his shoulder joint due to the weight if his arm is held at 30° below the horizontal?

A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg ∙ m² is rotating freely with an angular speed of 1.0 rad/s.Two people,each of mass 60 kg,are standing right outside the edge of the merry-go-round and suddenly step onto the edge with negligible speed relative to the ground.What is the angular speed of the merry-go-round right after the two people have stepped on?

A uniform rod weighs 40 N and is 1.0 m long.It is hinged to a wall at the left end,and held in a horizontal position at the right end by a vertical string of negligible weight,as shown in the figure.What is the magnitude of the torque due to the string about a horizontal axis that passes through the hinge and is perpendicular to the rod? The hinge is very small with negligible friction.