An ant of mass m clings to the rim of a flywheel of radius r, as shown above. The flywheel rotates clockwise on a horizontal shaft S with constant angular velocity 𝜔 . As the wheel rotates, the ant revolves past the stationary points I, II, III, and IV. The ant can adhere to the wheel with a force much greater than its own weight.

It will be most difficult for the ant to adhere to the wheel as it revolves past which of the four points?

• I

• II

• III

• IV

• It will be equally difficult for the ant to adhere to the wheel at all points.

Four round objects of equal mass and radius roll without slipping along a horizontal surface that then bends upward and backward into an arc of half a circle. The objects all have the same linear speed initially. The objects are a hollow cylinder, a solid cylinder, a solid sphere, and a hollow sphere. The objects to go up the arc and exit the arc going in the opposite direction they entered without falling off the arc. Now, several trials are run for each object. For each trial, the initial speed of the object is reduced until the object does not make it through the full arc. The speed needed for each object to just make it through the arc is recorded. Which of the following correctly lists the objects in order from fastest to slowest speed needed to make it through the arc?

• Hollow cylinder, hollow sphere, solid cylinder, solid sphere

• Hollow cylinder, solid sphere, solid cylinder, hollow sphere

• Solid sphere, solid cylinder, hollow sphere, hollow cylinder

• Solid sphere, hollow sphere, solid cylinder, hollow cylinder

• Hollow sphere, solid cylinder, hollow cylinder, solid sphere

Tags

NGSS.HS-PS2-1

A small solid sphere is released from rest at the top of an inclined plane as shown. The sphere rolls down without slipping and reaches the bottom of the plane. How would the angular momentum of the sphere at the bottom of the plane change if the coefficient of static friction between the sphere and the plane were increased?

• It would decrease because the force of friction would be greater.

• It would decrease because the net torque would be larger.

• It would increase because the angular acceleration would increase.

• It would increase because the linear acceleration would increase.

• It would remain the same because the net torque would remain the same.

Tags

NGSS.HS-PS2-1

A spool is made of two circular disks connected to the ends of a cylinder so that the centers of the disks and the cylinder are aligned. In the figure above, the cylinder is shown as the dashed circle, and the disk on one end of the cylinder is shown as the larger solid circle. The spool is at rest on a level horizontal surface. A string attached to the cylinder is pulled gently so that the spool can rotate without slipping on the surface at point P. A force F

is pulled in the direction of arrow d

, and the spool spins but does not roll across the table. If the string is pulled with a force of 2F

, which of the directions indicated, if any, indicates a pull on the string that will cause the spool to spin but not roll across the table?

• a

• b

• c

• d

• The spool will roll on the table for all four directions shown

Tags

NGSS.HS-PS2-1

A motor drives a shaft of radius R/8 that is attached to the center of a wheel of radius R. The motor is turned off, and the force that the motor exerts on the shaft, F_motor, varies with time, as shown. There is also a constant friction force of 0.4N applied to the rim of the wheel in the opposite direction of the motion. During which time interval does the rotational kinetic energy increase and then decrease?

• From t = 0 s to t = 1 s

• From t = 1 s to t = 3 s

• From t = 3 s to t = 5 s

• From t = 5 s to t = 7 s

• From t = 7 s to t = 8 s

Tags

NGSS.HS-PS2-1

NGSS.HS-PS2-2

Given the graph above of angular acceleration versus time for a rigid body rotating about a fixed axis, which segment of the graph represents the time interval during which the largest magnitude of net torque is exerted on the rigid body?

• Segment A

• Segment B

• Segment C

• Segment D

• Segment E

An ant of mass m clings to the rim of a flywheel of radius r, as shown above. The flywheel rotates clockwise on a horizontal shaft S with constant angular velocity 𝜔 . As the wheel rotates, the ant revolves past the stationary points I, II, III, and IV. The ant can adhere to the wheel with a force much greater than its own weight.

What is the magnitude of the minimum adhesion force necessary for the ant to stay on the flywheel at point III?

• mg

• m𝜔²r²

• m𝜔²r² + mg

• m𝜔²r - mg

• m𝜔²r + mg

Tags

NGSS.HS-PS2-1

A particle of mass m moves counterclockwise around a horizontal circle of radius r, as shown above. The angular speed of the particle is given as a function of time t by ω (t) = bt , where b is a positive constant and t ≥ 0.

What is the magnitude of the angular momentum of the particle about the center of the circle as a function of time?

• mbt/r

• mbrt

• mbr²t

• mbr²rt²

• mb²r²t²

A solid disk of mass M and radius R is freely rotating horizontally in a counterclockwise direction with angular speed ω about a vertical axis through its center with negligible friction. The rotational inertia of the disk is MR²/2. A second identical disk is at rest and suspended above the first disk with the centers of the two disks aligned, as shown in the figure above. There is no contact between the disks. The second disk is dropped onto the first disk, and after a short time they rotate counterclockwise with the same angular speed ωf.

The two disks are now shifted so that the axis of rotation goes through a point on the edge of the disks. The rotational inertia of the two-disk system is now

• 2MR²

• 3MR²

• 4MR²

• 5MR²

• 10MR²

Tags

NGSS.HS-PS2-2

The rotational inertia of a sphere of mass M and radius R about a diameter is 2/5 MR². The rotational inertia about an axis tangent to the sphere is

• 3/2 MR²

• 7/5 MR²

• MR²

• 1/2 MR²

• 2/5 MR²