A 60.0-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 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 m/s relative to Earth. How much work does the woman do to set herself and the turntable into motion?

Two identical uniform bricks of length $L$ are placed in a stack over the edge of a horizontal surface with the maximum overhang possible without falling, as in Figure. Find the distance $x$.

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 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 child’s centripetal acceleration?

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.

Eight-year-old Allie Oop, an aspiring basketball player, shoots five feet from the hoop. She is trying to get the ball above the rim, which is set at a height of 10 feet. She releases the ball from an initial height of 4 feet. The following equation models the path of the ball, where x is the horizontal distance in feet that the ball has traveled and h is the ball's height in feet above the ground.

$$h=-0.4 x^2+3 x+4$$

Allie practices her shot, but it never reaches the rim, so her father lowers the hoop to 9 feet. Now will the ball reach the height of the rim? Justify your answer.

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 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 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?

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.

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)?

A beetle sits near the rim of a turntable that rotates without friction about a vertical axis. The beetle then begins to walk toward the center of the turntable. As a result, does the angular speed of the turntable increase, decrease, or stay the same?

A waterwheel with diameter 12 ft turns at 0.3 rad/s}.

The waterwheel is connected by an axle to a grindstone with diameter 3 ft. What is the angular velocity of points on the rim of the grindstone?

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 $t = 4.0 \text{~s}$.