Compute the linear momentum and angular momentum of a Frisbee of mass 0.141 kg if it has a linear speed of 2.35 m/s and an angular velocity of 55.0 rad/s. Treat the Frisbee as a uniform disk of radius 15.5 cm.
Linear m v = .141 *2.35
angular I omega = (1/2)*.141* 0.155^2* (55)
To compute the linear momentum of the Frisbee, we can use the formula:
Linear Momentum = mass × linear speed
Given that the mass of the Frisbee is 0.141 kg and its linear speed is 2.35 m/s, we can substitute these values into the formula to find the linear momentum:
Linear Momentum = 0.141 kg × 2.35 m/s = 0.33135 kg·m/s
Therefore, the linear momentum of the Frisbee is 0.33135 kg·m/s.
Now, let's compute the angular momentum of the Frisbee. The formula for angular momentum is:
Angular Momentum = moment of inertia × angular velocity
Since the Frisbee is treated as a uniform disk, the moment of inertia can be calculated using the formula:
Moment of Inertia (disk) = (1/2) × mass × radius^2
Given that the mass of the Frisbee is 0.141 kg and the radius is 0.155 m (15.5 cm converted to meters), we can substitute these values into the moment of inertia formula:
Moment of Inertia (disk) = (1/2) × 0.141 kg × (0.155 m)^2 = 0.0013804875 kg·m^2
Now we can calculate the angular momentum by substituting the moment of inertia and the given angular velocity (55.0 rad/s) into the formula:
Angular Momentum = 0.0013804875 kg·m^2 × 55.0 rad/s = 0.07592 kg·m^2/s
Therefore, the angular momentum of the Frisbee is 0.07592 kg·m^2/s.