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.

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…

A flywheel is a solid disk that rotates about an axis that is perpendicular to the disk at its center. Rotating flywheels provide a means for storing energy in the form of rotational kinetic energy and are being considered as a possible alternative to batteries in electric cars. The gasoline burned in a 492-mile trip in a typical midsize car produces about 3.30 x 10° J of energy. How fast would a 26.8-kg flywheel with a radius of 0.315 m have to rotate to store this much energy? Give your answer in rev/min. Number 6640184.43 Units rev/min

0.5 m 2N A disk with radius of 0.5 m is free to rotate around its center without friction. A string wrapped around the disk is pulled, as shown above, exerting a 2 N force tangent to the edge of the disk for 1 s. If the disk starts from rest what is its angular speed after 1 s? O rad/s 1 rad/s 4 rad/s It cannot be determined without knowing the rotational inertia of the disk O A O B O D 3 4 6. 7. 8 9 10 11 Next acer Ce & 23 24 1 2 3 4. 6. 7 W e r y f a b C alt この * 00

The ramp on the figure is 0.75 m high. The object is a 2.0 kg cylinder with radius of r = 0.10 m. The cylinder rolls from the top and reaches the bottom. A) What is its total kinetic energy at the bottom? B) What is its rotational kinetic energy, C) what is its translational kinetic energy?

IA disk with moment of inertia I1 rotates about a frictionless, vertical axle with angular speed wi. A second disk, this one having moment of inertia I2 and initially not rotating, drops onto the first disk (see figure below). Because of friction between the surfaces, the two eventually reach the same angular speed ws. (a) Calculate wf. (b) Calculate the ratio of the final to the initial rotational energy. Before After

A disk of mass M and radius R sits on top of an incline of height h. From rest, it then rolls without slipping down the incline. h R The equation for conservation of energy as the disk falls down the incline is shown below: Initially, the disk only has potential energy given by Ma(h+ R). At the ground, the disk has a potential energy of MgR, and kinetic energy from rotational and translational motion. We then have Mg(h + R) = MgR+ /1w² + = M(Rw)², where I = MR². Calculate the angular speed of the disk as it rolls down the bottom of the incline. (Provide full solution of the problem).

In the figure, a thin uniform rod (mass 4.6 kg, length 5.5 m) rotates freely about a horizontal axis A that is perpendicular to the rod and passes through a point at a distance d = 1.9 m from the end of the rod. The kinetic energy of the rod as it passes through the vertical position is 16 J. (a) What is the rotational inertia of the rod about axis A? (b) What is the (linear) speed of the end B of the rod as the rod passes through the vertical position? (c) At what angle 0 will the rod momentarily stop in its upward swing? (a) Number Units (b) Number Units (c) Number Units B