The water side of the wall of a $100$-$\mathrm{m}$-long dam is a quarter circle with a radius of $10 \mathrm{~m}$. Find the hydrostatic force on the dam and its line of action when the dam is filled to the rim.

When the string is pulled with a force $p$ tangent to the rim, it gives the cylinder an angular acceleration $\alpha$, if the cylinder had fourfold the radius but everything else was the same the angular acceleration would be?

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 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?

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?

A carousel with a 50 -foot diameter makes 4 revolutions per minute. (a) Find the angular speed of the carousel in radians per minute. (b) Find the linear speed of the platform rim of the carousel.

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 50.0-kg child stands at the rim of a merry-go-round of radius 2.00 m, rotating with an angular speed of 3.00 rad/s. What is the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path?

A wheel of radius 1.5 m rotates at a uniform speed. If a point on the rim of the wheel has a centripetal acceleration of $1.2\ m/s^2,$ what is the point's tangential speed?

A dart is thrown horizontally with an initial speed of 10 m/s toward point P, the bull's-eye on a dart board. It hits at point Q on the rim, vertically below $P, 0.19$ s later. What is the distance $P Q$ ?

Solve the given problems.

Find the equation describing the rim of a circular porthole $2$ ft in diameter if the top is $6$ ft below the surface of the water. Take the origin at the water surface directly above the center of the porthole.

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?

A point on the rim of a flywheel with radius $1.50 \mathrm{ft}$ has a linear velocity of $30.0 \mathrm{ft} / \mathrm{s}$. Calculate the time for it to complete $4 \pi \mathrm{rad}$

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).