A 320 Newton frictional force acts on the rim of a 1.0 m diameter wheel to oppose its rotational motion. Find the torque about the wheel's central axis.

A firecracker, initially at rest, explodes into two fragments. The first, of mass 14 g, moves in the +x-direction at 48 m/s. The second moves at 32 m/s. Find the second fragment's mass and the direction of its motion.

An object initially at rest explodes into three fragments. The momentum vectors of two of the fragments are shown. Draw the momentum vector $\vec{p}_3$ of the third fragment.

A 5.00 kg firecracker that was initially at rest explodes into two parts: one part has a mass of 3.00 kg and moves at a velocity of 25.0 m/s towards the west. The other part has a mass of 2.00 kg. What is the velocity of the second piece as a result of the explosion?

a) -28.7 m/s

b) 15.8 m/s

c) -37.5 m/s

d) 43.2 m/s

A compact disc's rotation varies from about 200 rpm to 500 rpm. If the disc plays for 74 min, what's its average angular acceleration in

(a) rpm/s

(b) $\mathrm{rad} / \mathrm{s}^2$

Let R be the region completely enclosed by $y=2^x, y=3^x$, and x=3. Write an integral in one variable whose value equals the volume of the solid formed when R is revolved about the x-axis.

A point on the rim of a rotating wheel has nonzero acceleration, since it's moving in a circular path. Does it necessarily follow that the wheel is undergoing angular acceleration?

A string passing over a pulley has a $3.80-\mathrm{~kg}$ mass hanging from one end and a $3.15-\mathrm{~kg}$ mass hanging from the other end. The pulley is a uniform solid cylinder of radius $4.0 \mathrm{~cm}$ and mass $0.80 \mathrm{~kg}$.In fact, it is found that if the heavier mass is given a downward speed of $0.20 \mathrm{~m} / \mathrm{~s}$, it comes to rest in $6.2 \mathrm{~s}$. What is the average frictional torque acting on the pulley?

Blocks of mass 10 kg and 30 kg hang on either side of a pulley on a massless string. The pulley has a mass of 3 kg, a radius of 0.1 m, and a radius of gyration of 0.08 m. If the system has an acceleration of $3 \mathrm{~m} \mathrm{~s}^{-2}$, what torque is exerted by the frictional forces in the bearings of the pulley?

In Figure 10-46, the incline is frictionless and the string passes through the center of mass of each block. The pulley has a moment of inertia $I$ and radius $R$.

$(a)$ Find the net torque acting on the system (the two masses, string, and pulley) about the center of the pulley.

Let S be the solid obtained by rotating the region shown in the figure about the y-axis. Sketch a typical cylindrical shell and find its circumference and height. Use shells to find the volume of S. Do you think this method is preferable to slicing? Explain.

Let S be the solid obtained by rotating the region shown in the figure about the y-axis. Explain why it is awkward to use slicing to find the volume V of S. Sketch a typical approximating shell. What are its circumference and height? Use shells to find V.

Find the length of the curve $y^{2}=x^{3}$ from x = 1 to x = 4.

Find the length of the curve $y=x^{3 / 2}$ from x=1 to x=4.