Angular Acceleration.

[Lance WIlliam]

A circular saw blade completes 1200 revolutions in 40s while coasting to a stop after being turned off. Assuming constant deceleration, what are (a) the angular deceleration and (b) the initial angular speed?

Answer in RPM/S
Method I used: Change in theta is 1200
Time: 40s
final Vel.:0
Initial Vel.:?
Alpha:? Eqn Used: (change in theta)=(1/2)(Initial vel.+final vel.)*time
looking for inital speed:
1200=(1/2)(initial vel+0)40seconds
Take the vel. found and place into eqn:
looking for alpha:
final vel. =Initial vel.+alpha*time


I ended up getting 1.5 ...

 

[Doc Al]

looking for inital speed:
1200=(1/2)(initial vel+0)40seconds

This will give you the angular speed in rev/s.

Take the vel. found and place into eqn:
looking for alpha:
final vel. =Initial vel.+alpha*time

That will give you alpha in rev/s/s, not RPM/s like they want. (Convert the speed to RPM--rev/min, instead of rev/s.)

 

[baba89]

1.5=0+alpha*40s
1.5/40s=alpha
alpha=0.0375 RPM/s

(a) The angular deceleration is 0.0375 RPM/s.
(b) The initial angular speed is 30 RPM (calculated using the equation: initial vel. = (change in theta)/time = 1200/40 = 30 RPM).

 

[Moetasim]

(a) The angular deceleration can be calculated using the formula: alpha = (final velocity - initial velocity)/time. In this case, the final velocity is 0 (since the saw blade is coasting to a stop) and the initial velocity can be found using the formula: change in theta = (1/2)(initial velocity + final velocity)*time. Plugging in the values, we get: 1200 = (1/2)(initial velocity + 0)*40, which gives us an initial velocity of 60 RPM. Therefore, the angular deceleration can be calculated as: alpha = (0 - 60)/40 = -1.5 RPM/s.

(b) The initial angular speed is already calculated in part (a) and is equal to 60 RPM.