Moment of inertia

A baseball bat can be rotated around many different axes of rotation. Three such possibilities are shown in the image. Rank the moment of inertia from largest to smallest and overlap axes labels if the same.

(a)  

Given the same baseball bat and possible axes of rotation shown in the image, for which axis of rotation would it be the easiest to rotate the bat from rest?

• A

• B

• C

A girl spins around in a circle trying to make herself dizzy. Without changing her position, she starts spinning twice as fast. By how much did her rotational kinetic energy change?

• It doubled

• It quadrupled

• It halved

• It did not change

A solid sphere and a hollow sphere (spherical shell) of the same mass and same radius rotate with the same amount of kinetic energy. Which one is rotating faster?

• The solid sphere

• The hollow sphere

• Neither; they must be rotating at the same speed

You want to double the radius of a rotating solid sphere while keeping its kinetic energy constant. (The mass does not change.) To do this, the final angular velocity of the sphere must be

• 4x its initial value

• 2x its initial value

• the same as its initial value

• half of its initial value

The three objects shown here all have the same mass and the same outer radius. Each object is rotating about its axis of symmetry (shown in blue). All three objects have the same rotational kinetic energy. Which object is rotating fastest?

• Object A

• Object B

• Object C

• All objects rotate at the same rate

A thin, very light wire is wrapped around a drum that is free to rotate. The free end of the wire is attached to a ball of mass m. The drum has the same mass m. Its radius is R and its moment of inertia is I = (1/2)mR². As the ball falls, the drum spins.

At an instant that the ball has translational kinetic energy K, what is the rotational kinetic energy of the drum?

• K

• 2K

• 0.5K

• 0.25K

Tags

NGSS.HS-PS3-1

Objects A, B, and C all have the same mass, all have the same outer dimension, and are all uniform. Rank these objects in order of their moment of inertia about an axis through its center (shown in blue), from largest to smallest.

• BCA

• ABC

• CAB

• BAC

Objects A, B, and C all have the same mass, all have the same outer dimension, and are all uniform. Each object is rotating about an axis through its center (shown in blue). All three objects have the same rotational kinetic energy. Rank these objects in order of their angular speed of rotation, from fastest to slowest.

• ABC

• CBA

• ACB

• BAC

Tags

NGSS.HS-PS3-2

1. Three uniform objects of the same mass M and radius R are spinning uniformly with the same angular velocity about their centers of mass. Object A is a sphere (I_sphere = (2/5)MR²); Object B is a solid cylinder (I_cylinder = 0.5MR²); and Object C is a ring (I_ring = MR²).  Which of them has the least rotational kinetic energy?

• The sphere

• The solid cylinder

• The ring

• All 3 have the same rotational kinetic energy