Lecture 20Monday October 20

Motion of a rigid bodyBody can translate only. In this case we can

replace the body by a point located at the center of mass.

Body can rotate about a fixed point. Can no longer represent body by just a point.

Body can translate and rotate.Rigid body means all points have the same

angular velocity, ω, about the axis of rotation.

Uniform Rotationω = constant

( ) it t

Rotation with angular accelerationNon-uniform angular motion

2

Angular acceleration :

If = constant

( )

1( )

2

f i

i

i i

d

t dt

t t

t t

Linear vs. Rotational MotionLinear variablePosition x(t)Velocity

Acceleration

Circular variablePosition θ(t)Velocity

Acceleration

( )( )x

x d tv t

t dt

( )( ) x xx

v dv ta t

t dt

( )( )

d tt

t dt

( )d t

t dt

Linear vs. RotationLinear

v constant

a constant

Rotationω constant

α constant

x v t

21

2i

v a t

x v t a t

t

21

2i

t

t t

AccelerationTwo components:

Centripetal, radially inwardTangential (rate at which particle’s velocity

increases along the circular path)

2

c

v

r

( )t

v ra r r

t t t

What corresponds to Force for rotational motion?Torque—twisting

Which forces provides greater turning effectiveness to the bolt head?

φ

AB

C

SchematicallyComponent of force perpendicular to lever

arm (wrench handle) produces twist

Longer wrench handle produces larger twist.

φ

r

sinF F

F

r

Torque, τTorque, the measure of twist, is proportional

to the length of the wrench handle, r, to the component of the applied force F perpendicular to the handle or lever arm.

sinr F rF r F

Net TorqueIf all forces are in the same plane

1 2 3 ...NET