Angular kinematics

Angles, angular velocity and the link between rotation and linear speed at the end of a limb.

The outline, topic by topic

Each topic is weighted the way the exam weighs it.

Radian: what is it?
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The SI unit of angle: a full turn is 2π radians, or 360°.
1 radian is about 57°.
In tennis, why is a serve with a straight arm faster than with a bent arm?
- It lengthens the racket's radius of rotation
- It reduces the whole arm's moment of inertia
- It shortens the path the racket travels
- It lets the shoulder turn faster for the same effort
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It lengthens the racket's radius of rotation
v = ω × r: at equal angular velocity, a larger radius gives more speed. A straight arm actually increases the moment of inertia, which makes rotating harder: it wins through the radius.
Angular velocity: what is it?
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Angle covered per unit of time, in rad/s.
It describes how fast a limb rotates.
Why does the end of a golf club move much faster than the hands?
- The club head is heavier than the hands
- It is much farther from the axis of rotation
- Gravity speeds up the club head more
- The club is metal, stiffer than the arms
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It is much farther from the axis of rotation
v = ω × r: at equal angular velocity, linear speed grows with distance from the axis.