1. A fan blade is rotating with a constant angular acceleration of +10.0 rad/s?. At what point on the blade, as measured from the axis of rotation, does the magnitude of the tangential acceleration equal that of the acceleration due to gravity?
2. A planet orbits a star, in a year of length 4.39 x 10%, in a nearly circular orbit of radius 2.39 1011 m. With respect to the star, determine (a) the angular speed of the planet, (b) the tangential speed of the planet, and (c) the magnitude of the planet's centripetal acceleration.
3. star has a mass of 2.05 x 1030 kg and is moving in a circular orbit about the center of its galaxy. The radius of the orbit is 3.9 104 light-years (1 light-year = 9.5 x 1015 m), and the angular speed of the star is 2.2 x 10-15 rad/. (a) Determine the tangential speed of the star. (b) What is the magnitude of the net force that acts on the star to keep it moving around the center of the galaxy?
4. A ball of radius 0.200 m rolls with a constant linear speed of 2.52 m/s along a horizontal table. The ball rolls off the edge and falls a vertical distance of 2.40 m before hitting the floor. What is the angular displacement of the ball while the ball is in the air?
5. The drawing shows a uniform horizontal beam attached to a vertical wall by a frictionless hinge and supported from below at an angle 0 = 44 by a brace that is attached to a pin. The beam has a weight of 340 N. Three additional forces keep the beam in equilibrium. The brace applies a force P to the right end of the beam that is directed upward at the angle @ with respect to the horizontal. The hinge applies a force to the left end of the beam that has a horizontal component H and a vertical component V. Find the magnitudes of these three forces.
6. A man holds a 166-N ball in his hand, with the forearm horizontal (see the figure). He can support the ball in this position because of the flexor muscle force M, which is applied perpendicular to the forearm. The forearm weighs 20.9 N and has a center of gravity as indicated. Find (a) the magnitude of M and the (b) magnitude and (c) direction (as a positive angle counterclockwise from horizontal) of the force applied by the upper arm bone to the forearm at the elbow joint.
7. The figure shows a model for the motion of the human forearm in throwing a dart. Because of the force M applied by the triceps muscle, the forearm can rotate about an axis at the elbow joint. Assume that the forearm has the dimensions shown in the figure and a moment of inertia of 0.072 kg-m? (including the effect of the dart) relative to the axis at the elbow. Assume also that the force M acts perpendicular to the forearm. Ignoring the effect of gravity and any frictional forces, determine the magnitude of the force M needed to give the dart a tangential speed of 4.2 m/s in 0.14s, starting from rest.
8. The drawing shows the top view of two doors. The doors are uniform and identical. Door A rotates about an axis through its left edge, and door B rotates about an axis through its center. The same force is applied perpendicular to each door at its right edge, and the force remains perpendicular as the door turns. No other force affects the rotation of either door. Starting from rest, door A rotates through a certain angle in 2.50 s. How long does it take door B (also starting from rest) to rotate through the same angle?
9. 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 407-mile trip in a typical midsize car produces about 3.47 x 10 J of energy. How fast would a 46.9-kg flywheel with a radius of 0.206 m have to rotate to store this much energy? Give your answer in rev/min.
10. A bowling ball encounters a 0.760-m vertical rise on the way back to the ball rack, as the drawing illustrates. Ignore frictional losses and assume that the mass of the ball is distributed uniformly. The translational speed of the ball is 6.68 m/ at the bottom of the rise. Find the translational speed at the top.
11. A rotating door is made from four rectangular glass panes, as shown in the figure. The mass of each pane is 58.5 kg. A person pushes on the outer edge of one pane with a force of F = 101 N that is directed perpendicular to the pane. Determine the magnitude of the door's angular acceleration.
12. A block (mass = 1.5 kg) is hanging from a massless cord that is wrapped around a pulley (moment of inertia = 1.1 x 10-3kg m2), as the figure shows. Initially the pulley is prevented from rotating and the block is stationary. Then, the pulley is allowed to rotate as the block falls. The cord does not slip relative to the pulley as the block falls. Assume that the radius of the cord around the pulley remains constant at a value of 0.032 m during the block's descent. Find (a) the angular acceleration of the pulley and (b) the tension in the cord.
13. Conceptual Example 14 provides useful background for this problem. A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 119 kg m?. When one person is standing at a distance of 1.45 m from the center, the carousel has an angular velocity of 0.627 rad/s. However, as this person moves inward to a point located 0.617 m from the center, the angular velocity increases to 0.835 rad/s. What is the person's mass?