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## Physics library

### Course: Physics library>Unit 7

Lesson 1: Rotational kinematics

# Rotational kinematic formulas

AP.PHYS:
INT‑3.A.1.1 (LO)
David explains the rotational kinematic formulas and does a couple sample problems using them. Created by David SantoPietro.

## Want to join the conversation?

• At , how did the answer become -6.37 m/s^2? I substituted the same values in the exact same kinematics equation and I got -62.83 m/s^2. Did I possibly enter something wrong with my calculator (it was in radians mode).
• I know the answer to your question!

Ok, so when you put them into the calculator, ALWAYS PUT PARENTHESIS FOR PI!

It is so important! If you just divide -(40rad/s)^2 by 80pi (2*40pi), then you will get -62.8319...
If you divide -(40rad/s)^2 by (80pi), you will get the right answer -6.3662...
• At 11 minutes, why did you use the full 4m for R? When working the problem I assumed 4m to be diameter so I thought R would be equal to 2m?
• There is no diameter here. r is the distance from the pivot point to where the force is applied. It's 4 meters.
• At , How is the answer 160m/s ? where did the radians go? Why not 160m rad/ sec? Thanks.
• How can `(4m)(40rad/s)` be equal to `160m/s`? I know the numbers are correct, but units don't really work, it should be `rad×m/s`.
• As it happens, the
``rad``
can be ignored, because radians are at their heart a ratio. And ratios are unitless, because
`` 5 units / 10 units = 1/2 (unitless)``

But you can leave it there if you want, it is still technically correct.
A radian is based on the formula s = r(theta). We use radians because if we plug in s = rx, some multiple of the radius, we cancel r to get x = theta, and since x is just a constant multiple, we have unitlessly defined an angle, which is extremely useful compared to degrees, which are arbitrary and would mess up the formula for this if you were to use them.
• Where does the 4th kinematic formula comes from?
3 months ago by Roma

I have the same question. The 4th kinematic formula is v^2=V^2 +2ax. David showed 4 formulas at about , which he said only apply if acceleration is constant. Where does the last formula come from?
• The kinematic equations are a set of four equations that can be utilised to predict unknown information about an object's motion if other information is known. They can never be used over any time period during which the acceleration is changing. Each of the kinematic equations include four variables. If the values of three of the four variables are known, then the value of the fourth variable can be calculated. In this manner, the kinematic equations provide a useful means of predicting information about an object's motion if other information is known. For example, if the acceleration value and the initial and final velocity values of a skidding car is known, then the displacement of the car and the time can be predicted using the kinematic equations. Lesson 6 of this unit will focus upon the use of the kinematic equations to predict the numerical values of unknown quantities for an object's motion.
• What if the angular velocity is not constant? What would the new equations be? How would I derive them?
(1 vote)
• These formulas are for constant angular acceleration, not constant angular velocity. If the angular acceleration is not constant, then the only way to solve rotational kinematics questions would be to use calculus -- the equations would involve derivatives and integrals.
• Can these kinematic formulas also be used for the arc length, tangential velocity, and tangential acceleration? Or do you have to do all your calculations with theta, angular velocity, and angular acceleration and then just convert at the end?
• How can (4m)(40rad/s) be equal to 160m/s? I know the numbers are correct, but units don't really work, it should be rad×m/s.
(1 vote)
• Think of how a radian is defined? A radian is a distance along the circumference of a circle divided by the radius (a distance from the center of the circle to the circumference). So a radian per second is (m/m)/s = m/(m*s). When you multiply the m/(m*s) by the radius you have (m * m/)(m*s) = m/s.

• Where did the radians unit go? Why isn't it 160 (m rad)/s?
(1 vote)
• Radians are actually m/m where it is a ratio of distance around the circle over the radius of the circle so radians are unitless.