1)A point mass attached to a massless bar without a pivot at one end rotates uni

Question

1)A point mass attached to a massless bar without a pivot at one end rotates uniformly around the pivot point with a speed 20m/s at a radius of 6 m from the axis of rotation. What is the angular velocity of the mass?
a. 120 rads/s
b. 2.67 rads/s
c. 4.33 rads/s
d. 3.33 rads/s

2)A point mass attached to a masslsss bar with a pivot point at one end rotates uniformly around the pivot point with angular velocity of 50 rads/s at a radius of 8 m from the axis of rotation. what is the speed of the mass?
a. 760 m/s
b. 400 m/s
c. 6.25 m/s
d. 240 m/s

3)An object starting from rest undergoes an angular acceleration of 4 rad/s^2 for 101 s. Through what angle (how many degrees in total) does it turn during this time?
a. 1.17×10^6 degrees
b. 1.87×10^6 degrees
c. 2.04×10^4 degrees
d. 404 degrees

4)How many rotations does the object of the previous question undergo?
a. 3.25×10^3 rotations
b. 5.2×10^3 rotations
c. 57 rotations
d. 1 rotations

5)what final angular velocity does the object disscussed in the previous two questions attain?
a.1.17×10^6 rads/s
b. 404 rads/s
c. 525 rads/s
d. 4 rads/s

Explanation / Answer

1) angular velocity = v/r

angular velocity = 20/6

angular velocity = 3.33 rad/s

2)

speed =r * w

speed = 50 * 8

speed = 400 m/s

3)

for the angle

angle = 0.50 * a * t^2

angle = 0.50 * 4 * 101^2

angle = 2.04 *10^4 rad = 1.17 *10^6 degree

4)

rotations = 2.04 *10^4/(2pi)

rotations = 3.25 *10^3

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