Unit 7 - Rotation and Torque

Angular position

θ

radians

Angular displacement

Δθ

radians

Δθ= θf - θi

Angular velocity

⍵

rad/sec

Angular acceleration

⍺

rad/s/s

Counterclockwise rotation (CCW)

+

Clockwise rotation (CW)

-

• centripetal acceleration

• tangential acceleration

An object traveling in a circle has 2 types of acceleration

Centripetal acceleration

• changes object’s direction of velocity

• perpendicular to velocity

• points toward the center

Tangential acceleration

• changes magnitude of object’s velocity

• antiparallel or parallel to velocity

• tangent to the circular path

Torque

• The ability of a force to cause angular acceleration

• 𝜏

• Nᐧm

• 𝜏=rFsin(θ)

Torque due to gravity

𝜏 = r(mg)sin(θ)

Newton’s 1st Law for Rotation

• net torque will change its angular velocity

• net torque of 0 = no rotation or rotating at a constant angular velocity

Static equilibrium

Fx=0

Fy=0

𝜏=0

Newton’s 2nd Law for Rotation

𝜏net=I⍺

Rotational inertia

• property of an object

• depends on mass and how it is distributed

• I=mr^2

• The further the mass is “pushed out” from the axis, the greater the rotational inertia

s (linear position) =

θr

v =

⍵r

a =

⍺r