Mastering Physics 10

Rank these forces (A through F) on the basis of the magnitude of the torque they apply to the wrench, measured about an axis centered on the bolt.

What is the moment of inertia I of this assembly about the axis through which it is pivoted? Express the moment of inertia in terms of mr, m1, m2, and x. Keep in mind that the length of the rod is 2x, not x.

Suppose that the rod is held at rest horizontally and then released. (Throughout the remainder of this problem, your answer may include the symbol I, the moment of inertia of the assembly, whether or not you have answered the first part correctly.) What is the angular acceleration ? of the rod immediately after it is released? Take the counterclockwise direction to be positive. Express ? in terms of some or all of the variables mr, m1, m2, x, I, and g.

Let wheel 1 rotate at a constant angular speed ?1. Find the ratio ?1/?2 of the angular speed of wheel 1 to the angular speed of wheel 2.

The rotation of wheel 1 is caused by a torque ?1. Find the ratio ?1/?2 of the torque acting on wheel 1 to the torque acting on wheel 2.

If the power needed to rotate wheel 1 is P1, what is the ratio P1/P2 of the power of wheel 1 to the power of wheel 2

Now suppose that the gear system that you studied in Parts A, B, and C represents the gear wheels on a bicycle. Wheel 1 is connected to the pedals and wheel 2 to the rear bicycle wheel, as shown in the figure. (Figure 2) The gear ratio for this particular system is defined as g=rfrontrrear, that is, the ratio of the radius rfront of the front gear wheel to the radius rrear of the rear gear wheel. Part D A cyclist uses 27,000 joules per minute (this is about 385 food Calories per hour) to cycle at a constant pedaling rate of 450 radians per minute along a flat road using a gear ratio of 4. Find the torque ?rear exerted on the rear gear wheel.

When the cyclist encounters a steep hill, in order to maintain the same energy consumption and pedaling rate she changes her gear ratio to 0.7. Which of the following statements describes the change caused by the new gear ratio? The angular speed of the rear gear increases. The torque exerted on the rear gear wheel increases. The torque exerted on the front gear wheel increases. The power delivered to the rear gear wheel increases.

Does the pivot point (i.e., the triangle in the diagram upon which the ruler balances) exert a force on the ruler? Does it exert a nonzero torque about the pivot? yes/yes no/no yes/no no/yes

Although the pivot exerts a force on the ruler it does not exert a torque with respect to the pivot point. Why not? Because the exerted force is vertical. Because the distance from the exerted force to the pivot is zero. Because the exerted force is along the ruler.

Find the mass M2.

Find the total kinetic energy Ktot of the dumbbell. Express your answer in terms of m, v, Icm, and ?.Ktot =

The rotational kinetic energy term is often called the kinetic energy in the center of mass, while the translational kinetic energy term is called the kinetic energy of the center of mass. You found that the total kinetic energy is the sum of the kinetic energy in the center of mass plus the kinetic energy of the center of mass. A similar decomposition exists for angular and linear momentum. There are also related decompositions that work for systems of masses, not just rigid bodies like a dumbbell. It is important to understand the applicability of the formula Ktot=Kr+Kt. Which of the following conditions are necessary for the formula to be valid? Check all that apply. The velocity vector v? must be perpendicular to the axis of rotation. The velocity vector v? must be perpendicular or parallel to the axis of rotation. The moment of inertia must be taken about an axis through the center of mass.