Question

A bowling ball slides along a slick, level floor at 2 m/s without rotating. Then it reaches a non-slick portion on the floor and suddenly begins to roll without slipping. To cause the ball to rotate, the floor imparts both an impulse and an angular impulse on the ball, but it doesn’t do any work on the ball. The bowling ball is a 5 kg, 21 cm diameter solid sphere and the floor has negligible rolling friction. Show your work in all parts.

Part A) Find the speed of the center of the mass as it rolls without slipping.

Part B) Find the linear momentum of the ball as it rolls without slipping.

Part C) Find the angular momentum of the ball as it rolls without slipping.

Answer 1

here,

the initial speed of center of mass , u = 2 m/s

the mass of bowling ball , m = 5 kg

diameter , d = 21 cm

radius , r = d/2 = 10.5 cm

r = 0.105 m

a)

the speed of the center of mass be v

using conservation of energy

0.5 * m * u^2 = 0.5 * m * v^2 + 0.5 * ( I * w^2 )

0.5 * m * u^2 = 0.5 * m * v^2 + 0.5 * (0.4 * (m * r^2) * (v/r)^2 )

0.5 * 2^2 = 0.7 * v^2

v = 1.69 m/s

the speed of center of mass is 1.69 m/s

b)

the linear momentum , P = m * v

P = 5 * 1.69 kg.m/s = 8.45 kg.m/s

c)

the angular momentum , L = I * w

L = (0.4 * m * r^2) * ( v/r)

L = 0.4 * 5 * 0.105 * 1.69 kg.m^2 /s

L = 0.35 kg.m^2 /s