A solid 5.3 kg sphere of diameter 13 cm rolls up a ramp that is at 30° relative to the horizontal. At the bottom of the ramp the center of mass of the sphere has a translational speed of 1.2 m/s. a. What is the kinetic energy of the sphere at the bottom of the ramp? b. How far up the ramp does the sphere go? c. If the mass of the sphere doubles and the radius is tripled, how does the answer to part b change? Explain.

A typical small rescue helicopter has four blades: Each is 4.00 m long and has a mass of 50.0 kg. The blades can be approximated as thin rods that rotate about one end of an axis perpendicular to their length (I = (Ml^2)/3). The helicopter has a total loaded mass of 1000 kg.  a.) Calculate the rotational kinetic energy in the blades when they rotate at 300 rpm.  b.) Calculate the angular momentum of the four combined blades when they rotate at 300 rpm (Hint: Find the angular momentum for one blade and multiply it by 4).

7. You are asked to design a turntable that is 55.8 cm in diameter that has a kinetic energy of 0.250 J when it is turning at 45.0 rev/min. a. What must its moment of inertia be? b. If you make the turntable in the shape of a uniform solid disk, what mass would it have?

4. A pinball of mass M and radius R is pushed against a spring of spring constant k. The spring is compressed a distance D and the pinball machine ramp is inclined at an angle 0. The spring is then released. The pinball is a solid metal sphere that rolls without slipping. a. Determine the speed of the pinball as it leaves the spring. Hint: the spring force is not constant so you cannot use constant acceleration kinematics. Use conservation of mechanical energy instead. b. What is the distance that the pinball would go up the ramp before coming back down?

Ethan and Joseph are riding on a merry-go-round. Ethan rides on a horse at the outer rim of the circular platform, twice as far from the center of the circular platform as Joseph, who rides on an inner horse. i. When the merry-go-round is rotating at a constant angular speed, what is Ethan's angular speed? a. Twice Joseph's b. The same as Joseph's c. Half of Joseph's d. Impossible to determine ii. When the merry-go-round is rotating at a constant angular speed, describe Ethan's tangential speed from the same list of choices?

A 4m board weighing 60 N extends out over the edge of the table with 40% of the board's length off the table. How far beyond the table can a 20N cat walk before the board begins to tilt Meow, O A. 1.2 m О В. 1.5 m о С. 1.1 m O D. 1.4 m O E. None of the above

a. What is the angular velocity of the two after the collision?b. What is the kinetic energy before and after the collision?c. What is the total linear momentum before and after the collision?

If the axis of rotation is specified, which of the following statements is not true in regard to a rigid body? a. The distance between any chosen pair of points on the body remains the same. b. The angular velocity is always the same everywhere on the body. c. The angular acceleration is always the same everywhere on the body. d. The linear velocity at every point on the body is always the same. e. A rigid body does not permanently change its shape.

An child jumps on 0.25 m from the edge of the 50.0-kg merry-go-round, which has a 1.50 m radius. a) Calculate the rotational kinetic energy in the merry-go-round plus child when they have an angular velocity of 20 rpm if the system's inertia is 84.38 Nm. b. Using energy considerations, find the number of revolutions the child's father will have to push to achieve this angular velocity starting from rest if he pushes with a force of 250 N  c. Again, using energy considerations, calculate the force the father must exert to stop the merry-go-round in two revolutions.

A small 200 g ball and a small 800 g ball are connected by a 40-cm-long, 200 g rigid rod. How far is the center of mass from the 800 g ball? What is the rotational kinetic energy if the structure rotates about its center of mass at 100 rpm?