Rotational Motion

Comparison of Angular Motion with

One-dimensional Horizontal Motion

Distance traveled is replaced by the angle traveled around the circle.

Velocity is replaced by Angular Velocity.

Acceleration is replaced by Angular

Acceleration.

Comparison of Angular Motion with

One-dimensional Horizontal Motion

Rotational Motion

Any two points on a rigid rotating object have the same angular speed and angular acceleration.

If the points moved at different rates, the rotating object would become distorted and change shape.

Rotational Motion

Any two points on a rigid rotating object, at different distances from the axis of rotation, have DIFFERENT tangential speeds and tangential accelerations.

One point must travel a larger distance s, and must travel a faster tangential speed, or it will lag behind.

Rotational Motion

Tangential Speed (VT) is the instantaneous linear speed of an object traveling a linear distance s along a circular path.

The instantaneous linear speed of a point rotating about an axis.

Rotational Motion

Tangential Speed (VT) is the instantaneous linear speed of an object traveling a linear distance s along a circular path.

Tangential speed of an object is dependent on its angular speed and distance from the axis of rotation.

Equation: Units:

Rotational Motion

Tangential Acceleration (aT) is the rate of change in tangential speed.

The instantaneous linear acceleration of a point rotating about an axis.

Tangential acceleration of an object is dependent on its angular acceleration and distance from the axis of rotation.

Equation: units:

Rotational Motion

Centripetal acceleration (ac) is the acceleration of an object caused by its change in direction around an axis of rotation.

It caused by a centripetal force Fc and is directed toward the center of the circle along the radius.

V = Vf – Vi

for extemely small values of t approaching zero.Using tip-to-tail method.

V = ac directed toward center.

Rotational Motion

Rotational Motion

Centripetal acceleration (ac) is the acceleration of an object caused by its change in direction around an axis of rotation.

2C

2T

C

ra

rv

a

Rotational Motion

Centripetal acceleration (ac) is the acceleration of an object caused by its change in direction around an axis of rotation.

Equation: units:

2C

2T

C

ra

rv

a

Tangential and Centripetal Acceleration

• Tangential aT and centripetal aC acceleration are perpendicular to each other.

• Tangential acceleration aT is a measure of a change in speed.

• Centripetal acceleration aC is a measure of change in direction.

Tangential and Centripetal Acceleration

To find total acceleration of object, can use Pythagorean Theorem because Tangential aT and centripetal aC accelerations are perpendicular to each other.

T

C1

T

C

2T

2Ctotal

2T

2C

2total

aa

tan

aa

tan

aaa

aaa