Rotational Motion 212022 Rotational motion 1 Frame of

Rotational Motion 2/1/2022 Rotational motion 1

Frame of Reference n n Rigid Body Everything measured relative to an axis of rotation Rotational Motion: Axis is located within the rigid body u Circular motion: axis is outside of the body u 2/1/2022 Rotational motion 2

Types of Quantities n n 2/1/2022 Linear Quantities Angular Quantities Rotational motion 3

Position/Displacem ent n Linear Quantity Displacement = X= X-X 0 u Unit: Meter u n Angular Quantity r r Radian u = l/r u Units: ? u 1 radian = 57. 3 u Angular displacement= - 0 = u 2/1/2022 Rotational motion l 4

Velocity n Linear v = x/ t u Units: m/s u n Angular velocity = (omega) = / t u Units: radians/second u 2/1/2022 Rotational motion 5

Acceleration n Linear a = v/ t u Units: m/s 2 u n Angular acceleration = (alpha) = / t u Units: radians/second 2 u 2/1/2022 Rotational motion 6

Mass n Linear m u Units: Kg u n Angular Moment of Inertia =I u Units: varies u Will cover later u 2/1/2022 Rotational motion 7

Force n Linear Force- any push or pull u Units: Newtons u n Angular u Torque- the cross product of a force and the lever arm at which it is applied u =rx. F u Units: Nm or ft lbs 2/1/2022 Rotational motion 8

Torque (continued) n Force is perpendicular to the radius F r use: = r x F = r·F 2/1/2022 Rotational motion 9

Torque (continued) n At an angle n 2/1/2022 = r · Fsin Rotational motion 10

Net Torque n = net = cw + ccw r r r 2/1/2022 Rotational motion 11

Rotational Motion Part 2 2/1/2022 Rotational motion 12

Center of Mass n n 2/1/2022 Effective point that all forces act upon. “balance point” Rotational motion 13

Inertia n Linear Mass u Units: Kg u n Angular Moment of Inertia/Rotational Inertia – describes the distribution of mass for a given object - Or an object’s tendency to continue to rotate or remain at rest u I = mr 2 (Hoop) u Different for different objects u 2/1/2022 Rotational motion 14

Moment of Inertia (continued) n n n 2/1/2022 Single object moving in a circle Hoop Disc or Solid Cylinder Sphere Rod Through Center Rod Through End Rotational motion I = mr 2 I = ½mr 2 I = (2/5) mr 2 I = (1/12) m. L 2 I = (1/3) m. L 2 15

Kinetic Energy n Linear u n Angular u 2/1/2022 KE = ½ mv 2 KErot= ½ I 2 Rotational motion 16

Momentum n Linear u n Angular u n L = I Conservation of Angular Momentum u 2/1/2022 p = mv I =I 0 0 = constant Rotational motion 17

Vector Nature of Angular Quantities n n n 2/1/2022 Vectors: Displacement, velocity, acceleration, force, momentum, etc. Same quantities are vectors in the angular frame Right Hand Rule Rotational motion 18