Home / AP® Exam / AP® Physics 1 / Rolling AP  Physics 1 FRQ

Rolling AP  Physics 1 FRQ

Rolling AP  Physics 1 FRQ – Exam Style Questions etc.

Rolling AP  Physics 1 FRQ

Unit 6: Energy and Momentum of Rotating Systems

Weightage : 10-15%

AP Physics 1 Exam Style Questions – All Topics

Exam Style Practice Questions, Rolling AP  Physics 1 FRQ

Question

A billiard ball has mass M, radius R, and moment of inertia about the center of mass Ic = 2 MR²/5 The ball is struck by a cue stick along a horizontal line through the ball’s center of mass so that the ball initially
slides with a velocity vo as shown above. As the ball moves across the rough billiard table (coefficient of sliding friction μk), its motion gradually changes from pure translation through rolling with slipping to rolling without slipping.
a. Develop an expression for the linear velocity v of the center of the ball as a function of time while it is rolling with slipping.
b. Develop an expression for the angular velocity ω of the ball as a function of time while it is rolling with slipping.
c. Determine the time at which the ball begins to roll without slipping.
d. When the ball is struck it acquires an angular momentum about the fixed point P on the surface of the table.
During the subsequent motion the angular momentum about point P remains constant despite the frictional force. Explain why this is so.

Answer/Explanation

Ans:

a. \(\sum F\)= ma; Ff = μFN;
– μMg = Ma
a = –μg
v = v0 + at
v = v0 – μgt
b. τ = Iα where the torque is provided by friction Ff = μMg
    μMgR = (2MR2/5)α
α = (5μg/2R)
ω = ω0 + αt = (5μg/2R)t
c. Slipping stops when the tangential velocity si equal to the velocity of the center of mass, or the condition for
    pure rolling has been met: v(t) = ω(t)R
    v0 – μgt = R(5g/2R)t, which gives T = (2/7)(v0/μg)
d. Since the line of action of the frictional force passes through P, the net torque about point P is zero. Thus, the time rate of change of the angular momentum is zero and the angular momentum is constant.

Scroll to Top