AP Physics: Rotation Test Review

Inertia

100

Definition of inertia. (Not the equation)

What is resistance to acceleration?

200

I = mr²

What is the equation for the moment of inertia for a point particle (of mass m at radius r away from the axis of rotation)?

300

The inertia of a merry-go-round that has a mass of 2500-kg and a radius of 2.5 meters. 

(I = 1/2mr² for a solid cylinder).

What is 5200 N*m? 

(I = 1/3(2500)(2.5)^2)

400

How a figure skater or diver reduces their inertia, which allows them to increase their angular velocity during flips and spins.

What is reducing their radius by pulling their arms (and legs) closer to their body (center of mass)?

500

The value by which these objects (of similar mass and radius) are sorted from least to greatest: 

a medicine ball

a basketball

a dumbbell weight

a large tire.

What is moment of inertia?

Torque

100

According to Newton's second law in rotational form, the moment of inertia of an object times its angular acceleration is equal to this. 

What is the sum of torques applied to that object?

200

This is the meaning, in english, of Newton's second law for rotational motion.

What is "an object that is rotating will continue to rotate and an object at rest will stay at rest, unless a net torque acts on the object". 

(i.e. a change in rotational motion is cause by the application of a rotating force, torque).

300

If you want to make the tea-cup ride at an amusement park spin 4 times as fast (increasing angular acceleration), by what factor must you increase the torque applied to the spinning mechanism?

What is quadrupled or 4-times? Newton's 2nd Law tells us that torque = inertia x angular acceleration... so torque and angular acceleration are proportional, and the inertia of the ride is constant. So if you increase acceleration by a factor of 4, torque will also increase by a factor of 4.... 4(torque) = inertia x 4(angular acceleration)

400

A merry-go-round accelerates uniformly from rest and reaches an angular speed of 0.4 rad/s in the first 10 seconds. If the net applied torque is 2000N, this is the moment of inertia for the merry-go-round.

What is 50,000 kg*m^2? Torque = inertia x angular acceleration, acceleration is change in angular velocity over time (0.4 rad/s divided by 10 sec = 0.04 rad/s^2. Plug angular acceleration and torque into the equation to solve, inertia = torque/angular acceleration, 2000N/0.04 rad/s^2 = 50,000 kg*m^2)

500

A string is wrapped around a pulley with a radius of 0.05 m and an inertia of 0.2 kg*m^2. If the string is pulled with a force, F, the resulting angular acceleration of the pulley is 2 rad/s^2. This is the magnitude of the force.

What is 8 N? 

(Torque = inertia x angular acceleration torque = Force x radius x sin theta (and for a pulley, theta is 90, so sin90 = 1) set inertia x acceleration = force x radius and solve for force: force = (inertia x acceleration)/radius force = (0.2 x 2) / 0.05 = 8)

Rotational Dynamics

100

Consider the egg carton from Flipping Physics. The egg carton would be easier to balance if the eggs are placed at the far ends then if they are at the middle because of this.

What is the difference in rotational inertia? 

(Mass at the end has a greater inertia, and is thus more resistant to changes in motion, so once it was balanced it was easier to keep balanced. Putting the mass in the middle decreases the inertia, which would make the ruler easier to rotate, but not easier to balance (balancing is the same as keeping the object at rest))

200

Using a long, thin, handle screwdriver is better for prying open a can of paint, while using a short, thick handle screwdriver is better for unscrewing a rusted screw because of this.

What is torque? 

(The long handle = longer lever arm in relation to prying off the lid, and more torque The thick handle = wider radius, which is the "lever arm" for the screw, thus more torque)

300

This is why a gymnast might stretch their arms out to help them balance on a beam.

What is increased radius, and increased inertia?

400

Three children try and pull on a merry-go-round to make it rotate. The merry-go-round has a radius of 3.65 m. Two children pull with equal forces of 40N to the right (clockwise) and a third child tries to rotate the merry-go-round the other direction with a 60 N force at the same time. This is the net torque on the merry-go-round (including the direction it will turn).

What is -73 N*m?

(Net torque = sum of torques - counter clockwise is positive, and clockwise is negative. Net torque = -(3.65)(40) - (3.65)(40) + (3.65)(60) = - 73)

500

A string is wrapped around a pulley with a radius of 0.2 m and an inertia of .25 kg*m². The string is pulled with a force of 15 N, resulting in this angular acceleration.

What is 12 rad/s²? 

(Torque = Force x radius Torque = Inertia x angular acceleration so Force x radius = Inertia x angular acceleration)

Angular Momentum

100

This law of linear momentum also applies to angular momentum.

What is the Conservation of Momentum?

200

This is the equation that represents conservation of angular momentum.

What is I₁w₁ = I₂w₂? 

(The momentum before is equal to the momentum after - and momentum is = inertia x angular velocity)

300

For a single-point mass, the angular momentum is equal to the linear momentum times this.

What is the radius? 

(L = mvr)

400

A disk of mass m₁ = 12 kg and radius r₁ = 0.3 m spinning with an angular velocity of 15 rad/s lands on top of a disk with m₂ = 16 kg and radius r₂ = 1 m initially at rest. They are aligned on the same axis of rotation. This is the resulting angular velocity of the system. (I = (1/2) MR²)

What is 0.5 rad/s?

500

An Atwood machine is made using a pulley that has significant (non-negligible) mass m_p. A box of mass 9 kg is attached to one end by a massless string. If the pulley has a radius of 0.1 m, and experiences an angular acceleration of 3 rad/s², what is the mass of the pulley?

What is 590 kg?

Mystery Questions

100

The rotational kinetic energy of a figure skater is quadrupled when this is doubled.

What is a the radius (as represented by spreading out her arms? K = Iw, and I = mr^2; so 2r = 2^2 or 4 (if you double mass, kinetic energy is only doubled)

200

The kinetic energy of a can of soup when it reaches the bottom of an incline.

What is 1/2 mv^2 + 1/2 Iw^2 ? The kinetic energy of an object that rotates down an incline is equal to the linear kinetic energy of the center of mass, and the rotational kinetic energy of the object.

300

This is the equation you would use to determine the amount of power produced by the spinning fan of a boat motor.

What is P = torque x angular displacement divided by time or torque x angular velocity Power is the rate at which work is done, and for rotational motion, work = torque x angular disparagement, and angular displacement over time is also angular velocity

400

Reason why racing bikes have large-thin tires and off-road bikes have smaller-thicker tires (assume the actual mass of a tire is about the same).

What is rotational inertia and Newton's 1st law? The greater the inertia, the greater the resistance to change and the easier to balance.... so a large thin tire distributes the mass further away from the radius, while the off-road tire puts the mass closer to the center... racing bikes are meant to go fast on smooth, flat surfaces while off-road bikes need to be able to adjust to changing terrain, and a lower inertia means that it will be easier for you to change the motion of the tire.

500

Why the angular velocity of a planet changes as it moves closer/further from the sun.

What is conservation of angular momentum? Iw = Iw ... so as the planet gets closer, r gets smaller so I gets smaller and w must get faster/larger to conserve momentum.