The angular position of a point on the rim of a rotating wheel is given by $\theta = 4.0t - 3.0t^2 + t^3$, where $\theta$ is in radians and t is in seconds. What are the angular velocities at $t = 2.0 \text{~s}$.

The angular position of a point on the rim of a rotating wheel is given by $\theta = 4.0t - 3.0t^2 + t^3$, where $\theta$ is in radians and t is in seconds. What is the instantaneous angular acceleration at the beginning of this time interval?

The position of a particle moving along the x axis depends on the time according to the equation $x = ct^2 - bt^3$, where x is in meters and t in seconds. What are the units of constant c?

A particle moves along the x axis. Its position is given by the equation x = 2 + 3t − 4t2, with x in meters and t in seconds. Determine (a) its position when it changes direction and (b) its velocity when it returns to the position it had at t = 0.

The angular position of a point on the rim of a rotating wheel is given by $\theta = 4.0t - 3.0t^2 + t^3$, where $\theta$ is in radians and t is in seconds. What is the average angular acceleration for the time interval that begins at $t = 2.0 \text{~s}$ and ends at $t = 4.0 \text{~s}$?

You are analyzing the motion of a large flywheel that has radius 0.800 m. In one test run, the wheel starts from rest and turns with constant angular acceleration. An accelerometer on the rim of the flywheel measures the magnitude of the resultant acceleration a of a point on the rim of the flywheel as a function of the angle $\theta-\theta_{0}$ through which the wheel has turned. You collect these results:

$$\begin{matrix} \mathrm{\theta-\theta_{0}(\mathrm{rad})} & \text{0.50} & \text{1.00} & \text{1.50} & \text{2.00} & \text{2.50} & \text{3.00} & \text{3.50} & \text{4.00}\\\mathrm{a\left(\mathrm{m} / \mathrm{s}^{2}\right)} & \text{0.678} & \text{1.07} & \text{1.52} & \text{1.98} & \text{2.45} & \text{2.92} & \text{3.39} & \text{3.87}\\\end{matrix}$$

Construct a graph of $a^{2}\left(\operatorname{in} m^{2} / s^{4}\right)$ versus $\left(\theta-\theta_{0}\right)^{2}$ in $\left(\mathrm{rad}^{2}\right)$. When the flywheel has turned through an angle of $90.0^{\circ}$, what is the angle between the linear velocity of a point on its rim and the resultant acceleration of that point?

A uniform sphere with mass $28.0 \mathrm{~kg}$ and radius $0.380 \mathrm{~m}$ is rotating at constant angular velocity about a stationary axis that lies along a diameter of the sphere. If the kinetic energy of the sphere is $176 \mathrm{~J}$, what is the tangential velocity of a point on the rim of the sphere?

A merry-go-round has a radius of 2.0 m and a moment of inertia 300 kg·m². A boy of mass 50 kg runs tangent to the rim at a speed of 4.0 m/s and jumps on. If the merry-go-round is initially at rest, what is the angular velocity after the boy jumps on?

Suppose a bicycle wheel is rotated about an axis through its rim and parallel to its axle. Is its moment of inertia about this axis greater than, less than, or equal to its moment of inertia about its axle?

Viewed from above, a turntable rotates counterclockwise. The angular velocity vector is then (a) tangential to the turntable's rim, (b) out of the plane of the turntable, (c) counterclockwise, (d) none of the preceding.

An electric turntable $0.750$ m in diameter is rotating about a fixed axis with an initial angular velocity of $0.250$ rev$/$s and a constant angular acceleration of $0.900$ rev$/$s$^2$.
(d) What is the magnitude of the $\it{resultant}$ acceleration of a point on the rim at $t=0.200$ s?

A pebble is dropped into a water well, and the splash is heard $16 \mathrm{~s}$ later, as illustrated in the cartoon strip. Estimate the distance from the rim of the well to the water's surface.

In each of the following sentences, underline the subject once and the predicate twice. Part of the caldera around Vesuvius, known as the Somma Rim, was formed approximately 17,000 years ago.

A point on the rim of a $0.75$-m-diameter grinding wheel changes speed uniformly from $12$ m/s to $25$ m/s in $6.2$ s. What is the angular acceleration of the grinding wheel during this interval?