Hi.
DAY of SILENCE
The Three Accelerations
Angular Acceleration, alpha, in rad/s^2.
Tangential Acceleration, a sub t, in m/s^2.
Centripetal Acceleration, a sub c, in m/s^2.
How are the accelerations different from one another?
Let's start with their units.
Angular acceleration has angular units - rad/s^2.
Tangential Acceleration and Centripetal Acceleration both have linear units - m/s^2.
Angular acceleration is clearly different from the other two.
Now just tangential acceleration and centripetal acceleration.
How are tangential acceleration and centripetal acceleration different from one another?
Direction!
Tangential means tangent to a circle or arc.
Centripetal means "center seeking".
When an object is moving in a circle, its centripetal acceleration is
always directed inward toward the center of the circle.
When present, tangential acceleration is always tangential to the circle the object is moving along.
Therefore, centripetal acceleration and tangential acceleration are always perpendicular to one another.
Which accelerations are required for circular motion?
Can circular motion exist without centripetal acceleration?
No!
Centripetal acceleration causes tangential velocity to change direction and therefore causes circular motion.
Centripetal acceleration must be present in order to have circular motion!
Can circular motion exist without tangential acceleration?
Yes!
Tangential acceleration exists only if the magnitude of the tangential velocity is changing.
What about angular velocity?
If the angular velocity is constant,
the change in angular velocity is zero,
which means the angular acceleration is zero,
therefore the tangential acceleration is also zero.
And now, back to angular acceleration.
Angular acceleration is on a merry go round!
Angular acceleration, how are you?
"I am down."
Because you are angular and the other two accelerations are linear?
"No, because my angular velocity is up however,"
"the merry-go-round is slowing down. So angular acceleration is down."
"Also, angular acceleration applies to the whole rigid object."
"However, tangential and centripetal acceleration require a specific radius."
"I am just so different from the other two."
Let's review the linear accelerations.
Remember: Centripetal acceleration is inward and always present with circular motion.
Tangential acceleration is tangent to the circle described by the object
and only present when there is an angular acceleration.
Thank you very much for learning with us today, we enjoyed learning with you.
The End.
Day of Silence is a student-led national event organized in thousands of schools, bringing
awareness to the silencing effects of anti-LGBTQ name-calling, builling and harassment in schools.
Students from middle school to college take a vow of silence in an effort to encourage schools and
classmates to address the problem of anti-LGBTQ behavior by illustrating the silencing effect of bullying
and harassment on LGBTQ students and those perceived to be LGBTQ.
Day of Silence.org
What will you do to end the silence?