What Are the Solutions to These Circular Motion Problems?

[issh]

Homework Statement

Homework Equations

Centripetal Acceleration: a=v²/r or a=w²r
where a= Centripetal Acceleration
v= Linear Velocity
r= Radius
w=angular velocity

The Attempt at a Solution

Question Number 1: Drew a diagram of a circular with one point being O, another being P and another being A, Radius of Circle is 3.6m, and joined O and P to a 25^o
MIGHT BE WRONG

Question Number 2:
Turn of 90^o takes 0.4 seconds
Therefore 90degree/0.4 seconds = 225 degrees per second or
Therefore using equation
a=w²r
a=225²*0.45
a=22781.25degrees/sec

Pretty sure this is also wrong as for acceleration, it seems too fast

Question Number 3:
Drew diagram--> Circle[Radius 12 cm][2 Revolutions per second]
a=w²r


Question Number 4:
Honestly have no idea how to start

 

[Yuqing]

For 1, since the speed on and off the circular path remains constant, then the distanced traveled in an equal amount of time is identical. This means OA = OP. What remains is to calculate OP which can be done using simple circle geometry.

For 2 and 3, you look to be on the right track.

For 4, consider the block's motion. Since the car follows a circle of radius 150m at a speed of 8m/s the block must do the same. The string is the thing accelerating the block, so the angle will be such that the tension offers the suitable amount of centripetal acceleration.

 

[issh]

Thanks Yuqing
For question 1, pretty sure its correct!
Due to fact speed of object is identical(from OP to OA), and also same time, therefore DistanceOA = Distance OP

Find circumference of circle then find length of 25degree

Therefore
C(25degree)= 2*pi*3.6*(25/360)
C(25degree)=1.57m

Thanks

now for Q2-4!