A ball is rotating in a horizontal circle at the end of a string that is 3.2 m long at an angular velocity of 11.5 rad/s. The string is gradually shortened to 2.7 m without any force being exerted in the direction of the ball's motion.
A) Find the new angular velocity fo the ball in rad/s. (the ans. is not 13.63??).
B) Find its new linear speed in units of m/s. (36.8 is not right??).
2006-11-06 05:57:18 · 5 answers · asked by Mariska 2 in Science & Mathematics ➔ Physics
Use the conservation of angular momentum formula:
L1 = L2
A) (3.2)^2*11.5 = (2.7)^2*w2
w2 = 16.2rad/s
Linear speed = v = rw
v = 2.7*16.2 = 43.7m/s
2006-11-06 06:19:56 · answer #1 · answered by quark_sa 2 · 0⤊ 0⤋
The first two answers you received are not correct. You can demonstrate this to yourself by an experiment. For example, attach a weight to a string, put the string through the hole in a spool (of thread), start the weight revolving around the spool at the end of the string, and then pull the string in (through the spool). The RPM of the weight will increase DRAMATICALLY. It will be very apparent that you have increased its angular velocity significantly.
So what is the right answer?
I think that what stays the same is the object's angular momentum, which is its linear momentum (mv, mass times velocity) times the distance from the center of rotation.
The initial angular momentum is the mass (which is not given, and doesn't affect the answer) times linear velocity (which is the angular velocity in rad/s times the radius in m) times the radius.
Angular momentum = m x 11.5 rad/sec x 3.2 m x 3.2 m
= 117.76 x mass
After the string is shortened, we have mass x angular velocity x radius x radius = 117.76 x mass
Simplifying, angular velocity x 2.7^2 = 117.76
Solving, angular velocity = 117.76 / (2.7^2) = 16.15 rad/sec
At 16.15 rad/sec and a radius of 2.7 m, the velocity is 16.15 x 2.7 = 43.6 m/sec
Make sure that you use the correct number of significant digits in each of your answers.
2006-11-06 14:45:00 · answer #2 · answered by actuator 5 · 0⤊ 0⤋
The angular velocity does not change no matter what the radius of rotation is. it remains at 11.5 rad/s because no force was applied in the direction of ball's motion but linear velocity changes from 11.5*3.2=36.8 to 11.5*2.7=31.05
2006-11-06 14:16:01 · answer #3 · answered by Totok 2 · 0⤊ 0⤋
Use conservation of angular momentum:
I1w1 = I2w2
Where I1 = moment of inerita 1 = mr^2 = m(3.2^2)
I2 = moment of inertia afterwards = mr^2 = m(2.7^2)
w1 = 11.5 x 3.2
Solve for w2, the new angular velocity.
The new linear speed is then w2 x 2.7
2006-11-06 14:21:56 · answer #4 · answered by Jim C 3 · 0⤊ 0⤋
A) ang. velocity will remain constant because no force being exerted in the ball's direction of motion. i.e.. ans is 11.5 rad/s
B)new linear speed = 2.7 * 11.5 =______
2006-11-06 14:15:45 · answer #5 · answered by sandeep t 1 · 0⤊ 0⤋