Help A question on circular motion

[Kudo Shinichi]

Help!A question on circular motion

Homework Statement

a) A car is accelerated around a level circular track of radius 150 m. At time t=0 it has a speed of 15m/s and a total linear acceleration of 1.8m/s^2. Find its angular acceleration.
b)assume the angular acceleration remains constant at the value found in a). At what time will the car start to skid if the coefficient of friction between the tires and the road is 0.35.

The Attempt at a Solution

a) total distance: circumference: pi times diameter=pi times 300m=942.48m
average speed = (15+16.8)/2=15.9m/s
time used: 942.48/15.9=59.28s
acceleration= (v^2)/r=15.9^2/150=1.69m/s^2
b)
For this question I know that I need to find the mass for the car first, but I don't really know how to get the answer. After that I can use the equation:F=ma to get the force. then use several other equations to find the time

Thank you for helping me.

 

[alphysicist]

Hi Kudo Shinichi,

Homework Statement

a) A car is accelerated around a level circular track of radius 150 m. At time t=0 it has a speed of 15m/s and a total linear acceleration of 1.8m/s^2. Find its angular acceleration.
b)assume the angular acceleration remains constant at the value found in a). At what time will the car start to skid if the coefficient of friction between the tires and the road is 0.35.

The Attempt at a Solution

a) total distance: circumference: pi times diameter=pi times 300m=942.48m
average speed = (15+16.8)/2=15.9m/s
time used: 942.48/15.9=59.28s

I don't believe you need to find any sort of average speed for this part of the problem. Part a is asking about what happens at time t=0 and you know the speed at that time.

acceleration= (v^2)/r=15.9^2/150=1.69m/s^2

This is the right approach (but use the correct speed). What type of acceleration does this formula give, and how is it related to the total linear acceleration?

Once you have those, the question asks for the angular acceleration. What type of linear acceleration is that directly related to?

 

[Kudo Shinichi]

Hi Kudo Shinichi,



I don't believe you need to find any sort of average speed for this part of the problem. Part a is asking about what happens at time t=0 and you know the speed at that time.




This is the right approach (but use the correct speed). What type of acceleration does this formula give, and how is it related to the total linear acceleration?

Once you have those, the question asks for the angular acceleration. What type of linear acceleration is that directly related to?

acceleration= (v^2)/r=15^2/150=1.5m/s^2 This is the centripetal acceleration

1.8m/s^2=v^2/300
v=sqrt(1.8*300)=540
angular velocity =(2*pi* r) /v
=(2*pi*150)/540
=1.74
This is what I can think of...is it the right way to approach this question.

 

[LowlyPion]

acceleration= (v^2)/r=15^2/150=1.5m/s^2 This is the centripetal acceleration

1.8m/s^2=v^2/300
v=sqrt(1.8*300)=540
angular velocity =(2*pi* r) /v
=(2*pi*150)/540
=1.74
This is what I can think of...is it the right way to approach this question.

You are correct that is the centripetal acceleration. Unfortunately the question asks for angular acceleration. This is determined by Tangential acceleration/Radius.

For part b) how fast can the car go before skidding out? This depends on the radial acceleration exceeding the frictional hold on the tires. Once you find that speed then you can use the initial conditions to figure how long it takes.

 

[Kudo Shinichi]

You are correct that is the centripetal acceleration. Unfortunately the question asks for angular acceleration. This is determined by Tangential acceleration/Radius.

For part b) how fast can the car go before skidding out? This depends on the radial acceleration exceeding the frictional hold on the tires. Once you find that speed then you can use the initial conditions to figure how long it takes.

a) The equation for tangential acceleration is a=radius times alpha and alpha is the angular acceleration.
angular acceleration= (v^2)/r=15^2/150=1.5m/s^2
therefore, a=150*1.5=225m/s^2

for part b I still don't really get what you mean, you said find the speed, is it the average speed for this question or is it the velocity i get from the equation v= radius times omega, where omega equals to the angular velocity.

 

[alphysicist]

a) The equation for tangential acceleration is a=radius times alpha and alpha is the angular acceleration.
angular acceleration= (v^2)/r=15^2/150=1.5m/s^2

This is not angular acceleration (it does not have the correct units, for example). This is centripetal (or radial) acceleration.

Here are the three types of linear acceleration used for circular motion:

centripetal or radial acceleration (changes direction of velocity):
$$a_c = \frac{v^2}{r} = r\omega^2$$

tangential acceleration (changes speed):
$$a_{\rm tan} = r\alpha$$

total linear acceleration:
$$a_{\rm tot} = \sqrt{(a_{\rm tan})^2 + (a_c)^2}$$

and the problem is asking for the angular acceleration $\alpha$

 

[Kudo Shinichi]

For part b) how fast can the car go before skidding out? This depends on the radial acceleration exceeding the frictional hold on the tires. Once you find that speed then you can use the initial conditions to figure how long it takes.

I have found the acceleration for part a, which is 6.63x10^-3m/s^2, but I have some problems finding the time for part b can you explain more clearly. I think that what i need to find for this question is mass, because as soon as i have the answer for mass, i can find the force, and which i think can somehow relate the force with time.