1)
2) 2418 rad/s
3)
4) 36.3 m/s
Explanation:
1)
The angular acceleration of an object in rotation is the rate of change of angular velocity.
It can be calculated using the following suvat equation for angular motion:
where:
is the angular displacement
is the initial angular velocity
t is the time
is the angular acceleration
In this problem we have:
is the angular displacement
t = 1.3 ms = 0.0013 s is the time elapsed
is the initial angular velocity
Solving for , we find:
2)
For an object in accelerated rotational motion, the final angular speed can be found by using another suvat equation:
where
is the initial angular velocity
t is the time
is the angular acceleration
In this problem we have:
t = 1.3 ms = 0.0013 s is the time elapsed
is the initial angular velocity
is the angular acceleration
Therefore, the final angular speed is:
3)
The tangential acceleration is related to the angular acceleration by the following formula:
where
is the tangential acceleration
is the angular acceleration
r is the distance of the point from the centre of rotation
Here we want to find the tangential acceleration of the tip of the claw, so:
is the angular acceleration
r = 1.5 cm = 0.015 m is the distance of the tip of the claw from the axis of rotation
Substituting,
4)
Since the tip of the claw is moving by uniformly accelerated motion, we can find its final speed using the suvat equation:
where
u is the initial linear speed
a is the tangential acceleration
t is the time elapsed
Here we have:
(tangential acceleration)
u = 0 m/s (it starts from rest)
t = 1.3 ms = 0.0013 s is the time elapsed
Substituting,