Rotation Questions and Answers

A uniform solid sphere of unit radius is given translational velocity Vo and angular velocity wo and placed on rough surface as shown. If it comes to rest completely after moving some distance, then A. ω₀ = 5/7 V₀ B. ω₀ = 7/5 V₀ C. ω₀ = 5/2 V₀ D. ω₀ = 2/5 V₀

A block of ice and a solid uniform sphere, each having the same mass, start from rest at the same height h above the bottom of a hill and move down it. The ice slides without friction and the sphere rolls without slipping. Noting that the moment of inertia / for a solid sphere about an axis through its center is I = 2/5 MR²: a) What is the speed of each object as it reaches the bottom of the hill? b) Which object is moving faster at the bottom of the hill? c) Which object has more kinetic energy at the bottom of the hill?

A horizontal rod of mass 2 kg and length 1.5 m is free to rotate about a vertical, frictionless axle through its midpoint. Two forces are applied as shown in the figure below which is a view looking down on the rod from above. The 2 N force acts half way out from the point of rotation. The 3 N force acts at the end of the rod. What is the angular acceleration of the rod? A. 0.67 rad/sec^2 B. 4 rad/sec^2 C. 10 rad/sec^2 D. 8 rad/sec^2 E. None of these is within 3% of the correct answer.

A 10.0 kg mass is 25 centimeters from the pivot point on a balance scale. What mass must be placed 50 centimeters from the pivot to create rotational equilibrium?

A meter stick is being balanced on a triangular piece of wood, with two blocks hanging off of it, a block with a weight of 8.9 N is hanging 11 cm to the left of the pivot, and there is another block with an Unknown weight hanging 34 cm to the right of the pivot. What is the Unknown weight?

A uniform disk, a uniform hoop, and a uniform solid sphere of identical mass and radius are released at the same time at the top of an inclined ramp. They all roll without slipping. In what order do they reach the bottom of the ramp? A. disk, hoop, sphere B. hoop, sphere, disk C. sphere, disk, hoop D. sphere, hoop, disk E. hoop, disk, sphere

You have a hoop, but no scale with which to measure its mass. You do have a meterstick and a stopwatch. You determine that the radius of the hoop is 0.35 m. You also know that the force of friction between the hoop and the ground has a magnitude of 0.25 N from a previous experiment. You decide to start the hoop spinning and get it up to 7.9 rad/s and start it rolling. From the stopwatch you determine that the hoop takes 2.6 s to come to a stop. Calculate the mass of the hoop.

A disk-shaped merry-go-round of radius 2.63 m and mass 155 kg rotates freely with an angular speed of 0.631 rev/s. A 56.4 kg person running tangential to the rim of the merry-go-round at 3.41 m/s jumps onto its rim and holds on. Before jumping on the merry-go-round, the person was moving in the same direction as the merry-go-round's rim. What is the final angular speed of the merry-go-round? Express your answer in radians per second.

What is the ratio of the linear speed of ladybug 2 to that of ladybug 1?

To loosen the lid on a jar of jam 7.6 cm in diameter, a torque of 15 N·m must be applied to the circumference of the lid. If a jar wrench whose handle extends 14 cm from the center of the jar is attached to the lid, what is the minimum force required to open the jar?

Find the magnitude a of the angular acceleration of the cylinder as the block descends. Express your answer in terms of the cylinder's radius r and the magnitude of the free-fall acceleration g.

A thin hoop (m = 0.3 kg, r = 0.25 m) rolls without slipping down an incline. Its angular acceleration is 2 rad/s². a. What is the angle of the incline? b. What is the maximum value of the coefficient of static friction between the hoop and the incline?