What is the angular momentum (in kilogram-meter^2/second) of a 500.0 g ball rotating on the end of a string in a circle of radius 1.45 m at an angular speed of 1.50 rad/s?
L=Iω=mR²ω =0.5•1.45²•1.5 = 0.29 kg•²/s
A boy shoves his stuffed toy zebra down a frictionless chute, starting at a height of 1.49 m above the bottom of the chute and with an initial speed of 1.55 m/s. The toy animal emerges horizontally from the bottom of the chute and continues sliding along a horizontal surface with coefficient of kinetic friction 0.261. How far from the bottom of the chute does the toy zebra come to rest? Take g = 9.81 m/s2.
To calculate the angular momentum of a rotating object, we need to use the formula:
Angular momentum = (mass) × (velocity) × (radius)
In this case, the mass of the ball is 500.0 g, which is equivalent to 0.500 kg. The velocity is the tangential velocity, which can be calculated by multiplying the angular speed by the radius. So, the velocity is (1.50 rad/s) × (1.45 m) = 2.175 m/s.
Now, we can substitute the values into the formula:
Angular momentum = (0.500 kg) × (2.175 m/s) × (1.45 m)
Simplifying the calculation:
Angular momentum = 1.084 kg·m²/s
Therefore, the angular momentum of the ball is 1.084 kilogram-meter^2/second.