A2L Item 106
- Description: Find the ratio of tensions in a system of two masses rotating about a center.
- Goal: Hone rotational dynamics
- Source: UMPERG-ctqpe1246
- Keywords: Angular Velocity, Mechanics, Rotational Dynamics, Tension
The question for students:
A system consisting of two masses on a string is rotating with angular velocity ω on a frictionless horizontal surface. The center of rotation is the left-hand side of the string (nailed to the table).
The ratio of the tension in the inner string to that in the outer string is
- 0.25
- 0.5
- 1.5
- 2.0
- 3.0
- None of the above
Commentary for teachers:
Answer
(3) Many students think the ratio is determined just by the string lengths and give as an answer either (2) or (4). They fail to draw a free body diagram for the inner mass and, consequently, fail to realize that it is the net force on the inner mass that must maintain the circular motion of the inner mass.