**CHAPTER 10 HOMEWORK**

1. (p.270 Ex.9) (a) A 0.35-m diameter grinding wheel rotates at 2500rpm. Calculate its angular velocity in rad/s. (b) What is the linear speed and acceleration of a point on the edge of the grinding wheel?

2. (p.271 Ex.16) The angle through which a rotating wheel has turned in time *t
*is given by *q* = 6.0*t* - 8.0*t*^{2} + 4.5*t*^{4}*,
*where *q* is in radians and *t* in seconds. Determine an
expression (a) for the instantaneous angular velocity *w* and (b) for the
instantaneous angular acceleration *a*. (c) Evaluate *w* and *a *at
*t* = 3.0s. (d) What is the average angular velocity , and (e) the average
angular acceleration between *t* = 2.0s and *t* = 3.0s?

3. (p.271 Ex.24) Determine the net torque on the 2.0-m-long beam shown in Fig. 10-53. Calculate about (a) point C, the CM, and (b) point P at one end.

4. (p.272 Ex.29) A 2.4-kg ball on the end of a thin, light rod is rotated in a horizontal circle of radius 1.2m. Calculate (a) the moment of inertia of the ball about the center of the circle, and (b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a for of 0.020N on the ball. Ignore the rod's moment of inertia and air resistance.

5. (p.272 Ex.37) Two blocks are connected by a light string passing over a
pulley of radius 0.25m and moment of inertia *I*. The blocks move to the
right with an acceleration of 1.00m/s^{2} on inclines with frictionless
surfaces (see Fig. 10-57). (a) Draw free-body diagrams for each of the two
blocks and the pulley. (b) Determine *F*_{T1}* *and* F*_{T2},
the tensions in the two parts of the string. (c) Find the net torque acting on
the pulley, and determine its moment of inertia, *I .*

6. (p.273 Ex.45) Two uniform solid spheres of mass *M *and radius *R*_{0}
are connected by a thin (massless) rod of length *R*_{0} so that
the centers are 3*R*_{0} apart. (a) Determine the moment of inertia
of this system about an axis perpendicular to the rod at its center. (b) What
would be the percentage error if the masses of each sphere were s=assumed to be
concentrated at their centers and a very simple calculation made?

7. (p.274 Ex.65) Two masses, *m*_{1}* = *35.0kg and *m _{2}*
= 38.0kg, are connected by rope that hangs over a pulley (as in Fig. 10-60). The
pulley is a uniform cylinder of radius 0.30m and mass 4.8kg. Initially

*m*

_{1}

*is on the ground and*

*m*

_{2}rest 2.5m above the ground. If the system is released, use conservation of energy to determine the speed of

*m*

_{2}

*just before it strikes the ground. Assume the pulley bearing is frictionless.*

8. (p.275 Ex.73) A thin, hollow 60.0-g section of pipe of radius 10.0 cm starts rolling (from rest) down a 21.5° incline 5.60m long. (a) If the pipe rolls without slipping, what will be its speed at the base of the incline? (b) What will be its total kinetic energy at the base of the incline? (c) what minimum value must the coefficient of static friction have if the pipe is not to slip?

*9. (p.273 Ex.40) A thin rod of length *l* stands vertically on a table.
The rod begins to fall, but its lower end does not slide. (*a*) Determine
the angular velocity of the rod as a function of the angle *f*
it makes
with the tabletop. (*b*) What is the speed of the tip of the rod just
before it strikes the table?

*10 (p.273 Ex.51) Derive the formula given Fig. 10-21h for the moment of
inertia a uniform, flat, rectangular plate of dimensions *l* x* w*
about an axis through its center, perpendicular to the plate. (*b*) What is
the moment of inertia about each of the axes through the center that a re
parallel to the edges of the plate?