Rotational Motion of speed and a car

In summary, when a car is decelerating it's speed reduces from 80 km/h to 55 km/h. The wheels of the car complete 55 rotations during this time. The angular acceleration of the car is -1.5 rad/s^2. It would take 20 seconds for the car to stop if it continued in the same deceleration.
  • #1
kalupahana
36
0

Homework Statement


When a car is decelerating it's speed reduces from 80 km/h to 55 km/h. In this time the wheels of car complete 55 rotations. The diameter of the wheel is 1m.
Find the
1) angular acceleration of the car.
2) time taken to stop the car if it continued in same deceleration.


Homework Equations


v = rω
ω21 = ω20 + 2αθ
ω1 = ω0 + αt

Any equation regarding motion can be used to do this.
I used above three

The Attempt at a Solution


55 km/h = 15.2 m/s
80 km/h = 22.2 m/s

v = rω
I got ω = v/r from it. So
ω0 = 22.2 m/s
ω1 = 15.2 m/s

Then I used this equation to find angular acceleration
ω21 = ω20 + 2αθ

15.22 = 22.22 + 2 x 55 x π x α

-261.8 = 2 x 22/7 x 55 x α

α = -0.75 rad/s2

ω1 = ω0 + αt
can be use to find the time taken to stop

0 = 15.2 - 0.75t
t = 15.2/0.75 = 20.26 s


But in the textbook the answers are given as -1.5 rad/s2 for angular acceleration and 20 sec for time taken to stop. But I got other things.
Please help me to complete this.
Thnx
 
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  • #2
Assuming that they're actually asking for angular acceleration of each wheel, not the car - you seem to have erred in determining the angular displacement, as well as using the diameter of the wheel (instead of radius). Fixing those two errors gives the correct -1.5 rad/s^2 answer.

Your second part was done correctly, but you used the wrong values (found in the first part). Also - don't forget significant figures!
 
  • #3
What should I take as Angular displacement.
It makes 55 rotations during that decelerating time. One rotation is 2П. Then 55 rotations means 110П rotations.
When I use like this i got 0.34 rad/s^2.

You said that second part is correct. But how.
I used the data gain by the first part.(The angular acceleration as 0.75).
If it was incorrect 20 sec could not be get.

The angular acceleration -1.5 rad/s^2 can be gain by 0.75 x 2. Please explain me how did you reached to the answer.
 
  • #4
110pi rotations is right. But, you it appears that you still haven't corrected your angular velocities by using radius, as opposed to diameter. Using the equations you posted as "Relevant Equations" gives you the right answers.
 
  • #5
that means the radius is 1/2m.
Then velocities are come like 15.2 x 2 & 22.2 x 2.
Ok I understand. I'll try from it
 

Related to Rotational Motion of speed and a car

What is rotational motion?

Rotational motion is the movement of an object around an axis or fixed point. In the context of a car, it refers to the spinning of its wheels as it moves.

How is rotational motion different from linear motion?

Rotational motion involves movement around a fixed point or axis, while linear motion involves movement in a straight line. In a car, rotational motion is responsible for the spinning of the wheels, while linear motion is responsible for the forward movement of the car.

How is the speed of rotational motion measured?

The speed of rotational motion can be measured using angular velocity, which is the rate at which an object rotates around an axis. It is typically measured in radians per second.

How does rotational motion affect a car's performance?

Rotational motion is a crucial aspect of a car's performance as it is responsible for the rotation of the wheels, which provides the necessary traction for the car to move forward. A car's handling and stability are also affected by rotational motion.

What factors can impact the rotational motion of a car?

The rotational motion of a car can be impacted by several factors, such as the weight and distribution of the car, the condition and type of tires, and the engine power and torque. Friction and external forces, such as air resistance, can also affect the rotational motion of a car.

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