Compute the linear momentum and angular momentum
of a Frisbee of mass 0.160 kg if it has a linear speed of
2.00 m/s and an angular velocity of 50.0 rad/s. Treat the
Frisbee as a uniform disk of radius 15.0 cm.
p = m•v
L =I•ω = m•R^2•ω/2,
Linear momentum is given by the formula p = m * v, where p is the linear momentum, m is the mass of the object, and v is the linear velocity. Therefore, the linear momentum of the Frisbee can be calculated as follows:
p = (0.160 kg) * (2.00 m/s)
p ≈ 0.32 kg·m/s
To find the angular momentum, we use the formula L = I * ω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. Since the Frisbee is treated as a uniform disk, the moment of inertia can be expressed as I = (1/2) * m * r^2, where r is the radius of the disk.
Given that the radius of the Frisbee is 15.0 cm and the mass is 0.160 kg, we can substitute these values into the formula:
r = 0.15 m
I = (1/2) * (0.160 kg) * (0.15 m)^2
I ≈ 0.0024 kg·m^2
Now, we can calculate the angular momentum:
L = (0.0024 kg·m^2) * (50.0 rad/s)
L ≈ 0.12 kg·m^2/s
Therefore, the linear momentum of the Frisbee is approximately 0.32 kg·m/s, and the angular momentum is approximately 0.12 kg·m^2/s.
To compute the linear momentum of the Frisbee, we use the formula:
Linear momentum = mass x linear velocity
Given:
Mass (m) = 0.160 kg
Linear velocity (v) = 2.00 m/s
Linear momentum = 0.160 kg x 2.00 m/s
Linear momentum = 0.320 kg·m/s
So, the linear momentum of the Frisbee is 0.320 kg·m/s.
To compute the angular momentum of the Frisbee, we use the formula:
Angular momentum = moment of inertia x angular velocity
The moment of inertia of a uniform disk is given by the formula:
Moment of inertia (I) = (1/2) x mass x radius^2
Given:
Mass (m) = 0.160 kg
Radius (r) = 15.0 cm = 0.15 m
Angular velocity (ω) = 50.0 rad/s
Moment of inertia = (1/2) x 0.160 kg x (0.15 m)^2
Moment of inertia = 0.0036 kg·m^2
Angular momentum = 0.0036 kg·m^2 x 50.0 rad/s
Angular momentum = 0.18 kg·m^2/s
So, the angular momentum of the Frisbee is 0.18 kg·m^2/s.
To compute the linear momentum of the Frisbee, we use the formula:
Linear Momentum = mass × linear speed
Given:
Mass (m) = 0.160 kg
Linear speed (v) = 2.00 m/s
So, linear momentum = 0.160 kg × 2.00 m/s = 0.320 kg·m/s
To compute the angular momentum, we can use the formula:
Angular Momentum = moment of inertia × angular velocity
The moment of inertia (I) for a uniform disk is given by:
I = (1/2) × mass × radius^2
Given:
Mass (m) = 0.160 kg
Radius (r) = 15.0 cm = 0.15 m
Angular velocity (ω) = 50.0 rad/s
Substituting these values into the moment of inertia formula:
I = (1/2) × 0.160 kg × (0.15 m)^2 = 0.0027 kg·m^2
Now, we can calculate the angular momentum:
Angular Momentum = 0.0027 kg·m^2 × 50.0 rad/s = 0.135 kg·m^2/s
Therefore, the linear momentum of the Frisbee is 0.320 kg·m/s, and the angular momentum is 0.135 kg·m^2/s.