rolling motion

Question 1

what is rolling motion? what is required for rolling motion?

Answer 1

• both rotation and linear motion
• friction is required to have both rotational and linear motion

Question 2

what is linear velocity?

Answer 2

velocity of center of mass

Question 3

what is the equation for total kinetic energy in rolling motion?

Answer 3

KE = 1/2mv^2 + 1/2Iω^2

Question 4

what is torque? what does it cause?

Answer 4

• rotational force
• causes objects to move in linear motion (rotation)

Question 5

what is the equation for torque?

Answer 5

T = rFsinθ

Question 6

what is the unit for torque? what kind of parameter is it?

Answer 6

• Nm
• vector

Question 7

what does it mean for torque if θ = 0

Answer 7

torque is 0

Question 8

what does it mean for torque if θ = 90

Answer 8

torque is maximum

Question 9

what is θ in the torque equation?

Answer 9

the angle between r and F

Question 10

when rolling two objects, one that is not rolling and one that is, which will reach the bottom first?

Answer 10

the mass that is not rolling because both objects start with the same potential energy which is converted to kinetic energy as they go down. The rolling object must split its kinetic energy between linear and rolling energy and the non-rolling object can put all of its kinetic energy into forward velocity

Question 11

what is a rigid body? give an example of a rigid body and a non-rigid body

Answer 11

• the object is said to be rigid if the position of molecules is not changing in rotational motion
• solids are rigid
• liquids are not rigid

Question 12

what is the equation for the time period of rotation?

Answer 12

T = 2π / ω

Question 13

what is the equation for the rotational inertia of a hoop around a central axis?

Answer 13

I = Mr^2

Question 14

what is the equation for the rotational inertia of a hoop cylinder around a central axis?

Answer 14

I = 1/2M ((r inner)^2 + (r outer)^2)

Question 15

what is the equation for the rotational inertia of a solid cylinder around a central axis?

Answer 15

I = 1/2Mr^2

Question 16

what is the equation for the rotation inertia of a solid cylinder around a central diameter?

Answer 16

I = 1/4Mr^2 + 1/12ML^2

Question 17

what is the equation for the rotation inertia of a thin rod around a central diameter?

Answer 17

I = 1/12ML^2

Question 18

what is the equation for the rotation inertia of a solid sphere around a central diameter?

Answer 18

I = 2/5Mr^2

Question 19

what is the equation for the rotation inertia of a thin sphere around a central diameter?

Answer 19

I = 2/3 Mr^2

Question 20

what is the equation for the rotation inertia of a hoop around a central diameter?

Answer 20

I = 1/2Mr^2

Question 21

what is the equation for the rotation inertia of a slab around a central diameter?

Answer 21

I = 1/12M (a^2 + b^2)