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?

Determine whether the given series converges or diverges. $\sum_{n=1}^{\infty} \frac{1}{n^{2} \sqrt{n}}$

A wheel of radius $20.0 \mathrm{~cm}$ starts from rest and makes $6.00$ revolutions in $2.50 \mathrm{~s}$. (a) Find its angular velocity in rad/s. (b) Calculate its angular acceleration. (c) Calculate the final linear speed of a point on the rim of the wheel. (d) Calculate the linear acceleration of a point on the rim of the wheel.

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.

Nineteen items on the rim of a circle of radius 1 are to be chosen. Show that, for any choice of these points, there will be an arc of (arc) length 1 that contains at least 4 of them.

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.

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. (b) How much work does the woman do to set herself and the turntable into motion?

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?

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 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 end of this time interval?

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?

A wheel with a 30-cm radius is rotating at a rate of 3 radians/sec. What is the linear speed of a point on its rim, in meters per minute?

Solve. Give answers to two significant digits. A merry-go-round 40 ft in diameter makes four revolutions every minute. What is the speed of a seat on the rim?

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