Problem finding tangential acceleration

[Roq]

Hello, I'm having problem finding tangential acceleration. I was trying to find some examples of this being done in my book and on the web, but I couldn't. So I hope someone can help me with this.

The problem is: "A point on a rotating turntable 20.0cm from the center accelerates from rest to a speed of 0.700 m/s in 1.75s. At t=1.25s, find the magnitude and direction of (a) the radial acceleration, (b) the tangential acceleration, and (c) the total acceleration of the point."

The book as only covered uniform acceleration at this point, so I assumed it was here although it did not say.

For part (a), to try and find the acceleration I did: .7m/1.75, and multiplied it by 1.25 to get the velocity at the time, getting .5 m/s. I divided -.5^2 by .2 (20 cm converted to m), getting -1.25 m/s^2. It asked for the direction, and I think the direction is given by the minus sign, indicating it is towards the center.
I am stuck on part (b). The formula for tangential acceleration is d|v|/dt, but I am unsure what formula that I have for velocity. In this case,
v = acceleration * time = 0.4m/s^2(t). So if I derived that I would get .4m/s^2. Is this the answer?

 

[Dick]

For a point in circular motion, all of the velocity is tangential. So you've already found the tangential acceleration when you found (.7 m/sec)/(1.75 sec) which gives .4 m/sec^2, and as you've assumed it's constant. You don't need that last calculation you did. It's redundant. BTW, the direction of the radial acceleration isn't really 'given by the minus sign'. You just put the minus sign in. In circular motion the radial acceleration is always 'towards the center'.

 

[m2003]

Dear student,

Thank you for reaching out for help with your problem finding tangential acceleration. I understand that this concept may be new to you, so I will try to explain it in a clear and simple way.

Tangential acceleration is the component of acceleration that is tangent to the circular path of an object. In your case, the object is a point on a rotating turntable. To find the tangential acceleration, you will need to use the formula a = v^2 / r, where a is the tangential acceleration, v is the tangential velocity (in this case, the speed of the point on the turntable), and r is the radius of the circular path.

Now, let's break down the problem step by step. First, we need to find the tangential velocity at t=1.25s. You have correctly calculated the tangential velocity at t=1.25s to be 0.5 m/s. Next, we need to find the radius of the circular path. The problem states that the point is 20.0cm from the center, which is equivalent to 0.2m. So, we can plug these values into the formula: a = (0.5 m/s)^2 / 0.2 m = 1.25 m/s^2.

Therefore, the magnitude of the tangential acceleration at t=1.25s is 1.25 m/s^2. As for the direction, since the point is accelerating from rest, the direction of the tangential acceleration will be in the direction of the tangential velocity, which is tangential to the circular path. This means that the direction is tangent to the path and points in the direction of the motion.

I hope this explanation helps you understand how to find tangential acceleration in this problem. Remember to always pay attention to the units and be consistent in your calculations. If you have any further questions, do not hesitate to ask for help.

Best of luck with your studies!

Sincerely,