The dial of a standard clock has a 10 -centimeter radius. One end of an elastic string is attached to the rim at 12 and the other to the tip of the 10-centimeter minute hand. At what rate is the string stretching at 12:15 (assuming that the clock is not slowed down by this stretching)?

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?

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?

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?

Three bicycle wheels have masses that are distributed in three different ways: mostly at the rim, uniformly, and mostly at the hub. The wheels all have the same mass. If equal torques are applied to them, which one will have the greatest angular acceleration? Which one will have the least?

A wheel has an angular acceleration of α = (0.5 θ) rad/s^2, where θ is in radians. Determine the magnitude of the velocity and acceleration of a point P located on its rim after the wheel has rotated 2 revolutions. The wheel has a radius of 0.2 m and starts at ω0 = 2 rad/s.

A $60.0-\mathrm{kg}$ woman stands at the rim of a horizontal turntable having a moment of inertia of $500 \mathrm{~kg} \cdot \mathrm{m}^2$ and a radius of $2.00 \mathrm{~m}$. The turntable is initially at rest and is free to rotate about a frictionless, vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of $1.50 \mathrm{~m} / \mathrm{s}$ relative to the Earth. (a) In what direction and with what angular speed does the turntable rotate?

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 $t = 2.0 \text{~s}$.

A flywheel with a radius of 0.300 m starts from rest and accelerates with a constant angular acceleration of $0.600 \mathrm { rad } / \mathrm { s } ^ { 2 }$. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim after it has turned through $60.0 ^ { \circ }$.

Linear vs. Angular Speed A wheel of radius 30 centimeters revolves at a rate of 10 revolutions per second. A dot is painted at a point $P$ on the rim of the wheel (see figure).

Use a graphing utility to graph the function in part (a).

A wheel has an angular acceleration of $\alpha=(0.5 \theta) \mathrm{rad} / \mathrm{s}^2$, where $\theta$ is in radians. Determine the magnitude of the velocity and acceleration of a point $P$ located on its rim after the wheel has rotated $2$ revolutions. The wheel has a radius of $0.2 \mathrm{~m}$ and starts from rest.

Circle the antecedent in each sentence, and underline the pronoun in parentheses that agrees with it.

Example: Where did your $\boxed{\text{{brothers}}}$ buy (his, $\underline{{their}}$) new skis?

The basketball hoop outside has icicles hanging from (its, their) rim.

A wheel of radius 30 cm is rotating at a rate of 2.0 revolutions every 0.080 s. (a) Through what angle, in radians, does the wheel rotate in 1.0 s? (b) What is the linear speed of a point on the wheel's rim? (c) What is the wheel's frequency of rotation?

A flywheel with a radius of 0.300 m starts from rest and accelerates with a constant angular acceleration of $0.600 \mathrm { rad } / \mathrm { s } ^ { 2 }$. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim after it has turned through $120.0 ^ { \circ }$.