Rotational Equations and Center of Mass

College and Engineering Physics

Quiz 8: Rotational Equations and Center of Mass

1

Rotational Equations and Center of Mass



2

Use one of the rotational constant acceleration equations. You have a wheel that starts at 10 rad/s. It accelerates with a rotational acceleration of-0.5 rad/s2.

What is the magnitude of its angular displacement after 20 s?



3

You see four cars from an airplane. Being bored you derive an equation for each of their positions. The first is x(t) = 2t+5. The second is x(t) = -6t-4. The third is y(t) = 4t. The fourth is x(t) = -4 and y(t) = 7t+5.

At time t = 0, what is the center of mass of the four car system?



4


At time t = 2, what is the center of mass of the four car system?



5


What is the speed of the center of the mass of this system?



6

A pole has a linear density of (0.3 x) kg/m.

If it has a length of 200 cm, where is the center of mass from the lighter end of the bat?



7

Which of the following is the rotational counterpart of force?

1.

2.

3.

4. I

5.

6. K

7. L



8

What is the name of the variable ?

1. Angular Acceleration

2. Moment of Inertia

3. Torque

4. Rotational Kinetic Energy

5. Angular Momentum

6. Angular displacement (angle)

7. Angular velocity

8. Angular Force



9

What is the magnitude of the force that the ball is putting on thecross-beam?

x

y

m = 200 kg



10

Given the board below and using the equation and assuming thatthe point of rotation is the one shown, what is the magnitude of the torquethat the ball is putting on the cross-beam?

R F

x

y

m = 200 kg

10 m

Point of rotation

30o



11

Given the board below and using the equation and assuming thatthe point of rotation is the one shown, what is the direction of the torquethat the ball is putting on the cross-beam?

1. i 3. j 5. k2. -i 4. -j 6. -k

R F

x

y

m = 200 kg

10 m

Point of rotation

30o



12

What keeps the truck from flipping over?

1. The tension in the cable2. The weight of the of the truck3. The torque from the cable4. The torque from the weight of the truck

x

y

m = 200 kg

10 m

Point of rotation

30o



13

What is the magnitude of the torque from the weight of the truck?

x

y

m = 200 kg

10 m

Point of rotation

30o



14

What is the direction of the torque from the weight of the truck?

1. i 3. j 5. k2. -i 4. -j 6. -k

x

y

m = 200 kg

10 m

Point of rotation

30o



15

If the truck weight 2000 kg, how far is the center of mass of the truck fromthe center of rotation?

x

y

m = 200 kg

10 m

Point of rotation

30o



16

Adding 100 kg to the mass of the ball, we change the total torque. If theentire truck rotates with an acceleration of 5 rad/s2, what is its moment ofinertia?

x

y

m = 200 kg

10 m

Point of rotation

30o



17

Using the moment of inertia from the last question and the angular acceleration of 5 rad/s2, what is the magnitude of the angular momentum of the truck after 10 seconds?

x

y

m = 200 kg

10 m

Point of rotation

30o



18

Using the moment of inertia from the last question and the angular acceleration of 5 rad/s2, what is the rotational kinetic energy of the truck after 10 seconds?

x

y

m = 200 kg

10 m

Point of rotation

30o



19

A spinning cue ball hits the eight ball in a game of billiards. Which of the following quantities are conserved?

1. Translational Velocity

2. Translational Momentum

3. Force

4. Translational Kinetic Energy

5. Angular Velocity

6. Angular Momentum

7. Torque

8. Rotational Kinetic Energy

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Rotational Equations and Center of Mass