Angular deceleration of wheels.

**becca** · February 14th 2011, 08:31 AM

Right, so I have been stuck on this question for a while now but not sure where to start. I'm almost pulling my hair out, any guidance or pointers would be appreciated.

I need to calculate the angular deceleration of wheels of a lorry. It needs to stop in 0.5km using constant braking force.

It's weight is 5 tonnes and velocity is 80 km h-1. The wheels are 1.5m in diameter.

So far I've worked out the deceleration of the lorry (-0.494 ms-2), the braking force required (-2.4kN), the time taken to come to rest (2024.29), and the initial angular velocity of the wheels (29.63 rad/s).

Just can't get my head around the "angular deceleration" part. Can someone please tell me where to start.

Regards,

Becca.

**Unknown008** · February 14th 2011, 10:27 AM

You can use the same formula as with linear speed acceleration/deceleration.

$v^2 = u^2 + 2as$

v = 0,
u = initial angular velocity
a = acceleration or deceleration
s = angular displacement

**becca** · February 14th 2011, 10:59 AM

Hi, thanks for the reply.

Could I use alpha=dw/dt?

**topsquark** · February 14th 2011, 11:37 AM

Originally Posted by Unknown008

You can use the same formula as with linear speed acceleration/deceleration.

$v^2 = u^2 + 2as$

v = 0,
u = initial angular velocity
a = acceleration or deceleration
s = angular displacement

Originally Posted by becca

Hi, thanks for the reply.

Could I use alpha=dw/dt?

You do not have d $\omega$ /dt in order to do this. However you have the initial angular speed (you know the radius of the wheel and the linear speed, so $v_0 = r \omega _0$ ). You know the final angular speed, and you know the angular distance the wheel has gone through. ( $s = r \theta$ ) So you can use the angular analogue of Unknonw008's equation: $\omega ^2 = \omega _0^2 + 2 \alpha \theta$ .

By the way, the two equations $v_0 = r \omega _0$ and $s = r \theta$ are known as the "rolling without slipping" conditions. There is one more: $a = r \alpha$ . Whenever a wheel is moving without slipping these relations relate the linear variables (s, v, and a) to the rotating variables ( $\theta$ , $\omega$ , and $\alpha$ .)

-Dan

**becca** · February 15th 2011, 09:05 AM

Hi Dan,

Thanks for the reply.

So using your formula for acceleration I get:

α=(ω_0^2- ω^2)/θ

α=(29.63-0)/6.28

α = -69.90 rad/s^2

p.s. what software/program do you use to display your formulas like you do?

Thanks,

Becca.

Thread: Angular deceleration of wheels.

LinkBack

Thread Tools

Display

Angular deceleration of wheels.

Similar Math Help Forum Discussions

Finding deceleration

[SOLVED] Rotating Wheels

[SOLVED] Rotating Wheels

Spinning Wheels

Three wheels rotating at different speeds.

Search Tags