Physics
Lesson 7-2: Tangential and Centripetal Acceleration Part 1
Objects in circular motion have a “tangential speed”. This is not the
“tangent” from trigonometry. Instead, it is the “tangent” from geometry that
intersects a circle at exactly one point.
Tangential Speed is an object’s linear speed along a line that is
tangent to its circular path.
Imagine two children spinning on a merry go round. If both are sitting the same distance from the
center as it spins, then they will both travel the same distance, s, and have the same tangential
speed.
If one child sits near the edge and the other sits near the center, then which one travels a greater
distance?
In this situation, how will the tangential speeds compare?
Tangential Speed
vt = rω
tangential speed = radius x angular speed
Be aware that ω must be measured in radians when using this formula.
Example 1: A golfer has a maximum angular speed of 6.3 rad/s for her swing. She can choose
between two drivers, one placing the head of the club 1.9 m from her axis of rotation and the other
placing it 1.7 m from the axis.
a. Find the tangential speed of the club head for each driver.
b. All other factors being equal, which driver is likely to hit the ball farther?
Example 2: A pog disk rolls on its edge with an angular speed of 44.5 rad/s. If the radius of the
pog is 1.75 cm, what is the tangential speed of the pog’s rim?
The instantaneous linear acceleration of an object directed along the tangent to the object’s
path is the object’s Tangential Acceleration. The equation for this acceleration can be derived
by dividing both sides of the tangential speed equation by t.
Tangential Acceleration
at = rα
tangential acceleration = radius x angular acceleration
Example 3: A yo-yo has a tangential acceleration of 0.98 m/s2 when it is released. The string is
wound around a central shaft of radius 0.35 cm. What is the angular acceleration of the yo-yo?
Example 4: A centrifuge starts from rest and accelerates to 10.4 rad/s in 2.3 s. What is the
tangential acceleration of a vial that is 4.7 cm from the center?
Homework: Read pages 253-256 and complete Problem 7E and 7F