A 23-cm-long pen is tossed up in the air, reaching a maximum height of 1.7 m above its release point. On the way up, the pen makes 2 revolutions. Treating the pen as a thin uniform rod, calculate the ratio between the rotational kinetic energy and the translational kinetic energy at the instant the pen is released. Assume that the rotational speed does not change during the toss. The moment of inertia of the rod with axis through the center of mass is determined by ImL² where m is its mass and L is its length.
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- You are riding your bicycle down the street at a speed of 14 m/s. Your bicycle's frame has a mass of 6.6 kg, and each of its two wheels has mass 2.2 kg and radius 0.35 m. Each wheel can be thought of as a hollow hoop (assuming that the rim has much larger mass than the spokes). What is the total kinetic energy of the bicycle (in Joules), taking into account both the translational and rotational motion?A 20cm radius turn-table is turning with a constant angular speed ω0=33rev/min . The turn-table has a moment of inertia I=5.0kg(cm)2 relative to the axis through its center. Call this central axis the z-axis. A piece of sticky gum with mass m=50g falls straight down on the turn-table and sticks at a distance of 10cm from the center. What are the forces the tact on the system after the gum falls on the turn-table? Group of answer choices Weight of turn-table, Normal force on the turn-table, Weight of gum Weight of turn-table, Normal force on the turn-table, Weight of gum, Normal force on gum Weight of turn-table, Weight of gum Weight of gum What can you say about the net torque relative to the axis of rotation, after the gum falls on the turn-table? Group of answer choices there is a torque of 0.049 kg m2/s2, in the z direction there is a torque of 0.098 kg m2/s2, in the z direction there is no net torque in the z direction What is the angular momentum…A thin, uniform rod has one of its end mounted at 3. point P and is free to rotate about an axle that passes through P in a direction perpendicular to the figure. The rod is of length 1.0 m and mass 0.3 kg. It is released from rest at the horizontal position shown in the figure. A small ball of mass 0.1 kg is placed on a frictionless floor 1.0 m below point P such that when the rod reaches the vertical position, it just hits the ball. Assume that once the rod hits the ball, they stick together and swing up until they come to a momentary stop at an angle 0. (a) perpendicular to the figure? You can check the table on slide 27 of the lecture notes if needed. (b) problem from the perspective of energy conservation] (c) analyze the problem from the perspective of conservation of angular momentum] What is the rotational inertia of the rod about the axle passing through P and What is the angular speed of the rod just before it hits the ball? [Hint: analyze the What is the angular speed of the…
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