A spinning top has a diameter of 10 cm. A point on the outer rim of the top moves through an angle of 8¶ radians each second. A) what is the angular velocity of the point? B) what is the distance moved by the point in 5 seconds? C) what is the velocity of the point? D) what is the acceleration of the point?

step by step

R = 0.05 meter

A. You already said omega = 8 pi radians/second

C. omega R = v = 8 pi (0.05)

B. theta = angle moved = (8 pi)(5)
so distance = R Theta = (0.05)(8 pi)(5)

D. Ac = R omega^2 = 0.05 (64 pi^2)

I donot gate explained answer

a .8 rad / sec

b. ፀ = tw = 5s x 8pi rad/s = 40pi rad
c. V= r w= 0.05 x 8 = 0.4
d. a= v squre/r =0.16/ 0.05 = 3.2

Why did you say omega is 8πrad/SCE?

Knowledge

A, 8pi rad/s

B, 40rad.

to get answer

a,8¶r per s=4r/s b/s 1revo =360°=2¶r so

W=4rad/s
b,teta= wt=4rad/s*5s=20rad
C,v=wr=4rad/s*0.05m= 0.2m/s
d,a=w^2*r=16*0.05=0.8m/s^2

To solve these questions, we need to use some basic formulas related to angular motion. Let's go through each question step by step:

A) To find the angular velocity of the point, we can use the formula:
Angular velocity (ω) = Angle (θ) / Time (t)

Given that the point moves through an angle of 8π radians each second, we can substitute these values into the formula:
ω = 8π radians / 1 second
ω = 8π radians/s

Therefore, the angular velocity of the point is 8π radians/s.

B) To find the distance moved by the point in 5 seconds, we can use the formula:
Distance (s) = Radius (r) * Angle (θ)

We are given the diameter of the spinning top, so we need to calculate the radius first:
Radius (r) = Diameter (d) / 2
r = 10 cm / 2
r = 5 cm

Now we can substitute the values into the formula to find the distance moved by the point:
s = 5 cm * 8π radians
s = 40π cm

Therefore, the distance moved by the point in 5 seconds is 40π cm.

C) To find the velocity of the point, we can use the formula:
Velocity (v) = Radius (r) * Angular velocity (ω)

Substituting the values we know:
v = 5 cm * 8π radians/s
v = 40π cm/s

Therefore, the velocity of the point is 40π cm/s.

D) To find the acceleration of the point, we need to differentiate the angular velocity:
Acceleration (a) = d(ω) / dt

Since the angular velocity is constant, the acceleration is zero. This implies that the point is moving with constant velocity, as there is no change in its speed or direction.

Therefore, the acceleration of the point is zero.