the law of motion?

Question

an antique carousel that's powerd by a large electric motor undergoes constant angular acceleration from rest to full rotational speed in 5 sec. when the ride ends, a brake causes it to decelerate steadily from full rotational speed to rest in 10 secs. compare the torque that starts the carousel to the torque that stops it.

Answer 1

let τ = torque
α = angular acceleration = ∂ω / ∂t
ω = angular velocity.
∂ω / ∂t = change in angular velocity with respect to time
since α = constant, ∂ω / ∂t = ∆ ω / ∆ t
I = moment of inertia for the carousel.

by definition,

τ = I x α = I x (∆ ω / ∆ t)

where the "x" is "cross product" (google that if you don't understand)

for the case where the carousel is accelerating,

τ = I x ( (ωmax - 0)/ 5) = I/5 x ωmax

for the case where the carousel is slowing down

τ = I x ( (0 - ωmax)/ 10) = I/10 x (-ωmax)

in other words, the torque during acceleration is 2 x's the torque during deceleration.

since the function is "cross product", the torque during acceleration is a vector in the opposite direction of the torque during deceleration.

Answer 2

torque is the rate of change of angular momentum, so as the carousel gets from zero to full in five seconds, and full to zero in 10, the motor has twice the torque of the brake. It aslo as a the opposite sign, as one is a positive acceleration, and the other is a negative decceleration.

PS Jack & Doug have it right, (except they forgot the -ve bit) and Doug is right about assumning that the mass stays the same.

Answer 3

Assuming that nobody gets on or off while it's moving, the starting torque is twice the stopping torque.

Doug

Answer 4

It is called friction...


Newtons law states that an object in motion will remain in motion until an outside force acts upon it... in this case... friction...

Newtons law is also talking about inertia...
and momentum...
An object that has a momentum take the same amount of opposing force to stop it...

But most of the opposing force is lost due to heat...

Answer 5

It's double.