Compute the linear momentum and angular momentum of a Frisbee of mass 0.175 kg if it has a linear speed of 1.65 m/s and an angular velocity of 61.5 rad/s. Treat the Frisbee as a uniform disk of radius 12.0 cm.
Linear momentum
p=mv=0.175•1.65=0.289 kg•m/s
Angular momentum
L=I•ω=(mr^2/2) •ω=(0.175•(0.12)^2/2) •61.5=77.5 kg•m^2/s
To compute the linear momentum, we'll use the formula:
Linear momentum (p) = mass (m) × linear velocity (v)
Given that the mass of the Frisbee is 0.175 kg and the linear speed is 1.65 m/s, we can substitute these values into the formula to find the linear momentum:
p = 0.175 kg × 1.65 m/s
p = 0.28875 kg·m/s
Therefore, the linear momentum of the Frisbee is 0.28875 kg·m/s.
To calculate the angular momentum, we'll use the formula:
Angular momentum (L) = moment of inertia (I) × angular velocity (ω)
The moment of inertia for a uniform disk is given by the formula:
I = (1/2) × mass (m) × radius (r)^2
Given that the mass of the Frisbee is 0.175 kg and the radius is 12.0 cm (or 0.12 m), we can calculate the moment of inertia:
I = (1/2) × 0.175 kg × (0.12 m)^2
I = 0.00126 kg·m^2
Substituting the values of moment of inertia and angular velocity (61.5 rad/s) into the formula for angular momentum, we can now calculate the angular momentum:
L = 0.00126 kg·m^2 × 61.5 rad/s
L = 0.07749 kg·m^2/s
Therefore, the angular momentum of the Frisbee is 0.07749 kg·m^2/s.
To compute the linear momentum and angular momentum of the Frisbee, we first need to define the formulas for linear momentum and angular momentum.
Linear momentum (p) is given by the equation:
p = m * v
where p is the linear momentum, m is the mass, and v is the linear velocity.
Angular momentum (L) is given by the equation:
L = I * ω
where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
Now let's compute the linear momentum:
Given:
Mass (m) = 0.175 kg
Linear speed (v) = 1.65 m/s
Using the formula:
p = m * v
Substituting the values, we have:
p = 0.175 kg * 1.65 m/s
Calculating the result, we find that the linear momentum is 0.28875 kg·m/s.
Next, let's compute the angular momentum:
Given:
Radius (r) = 12.0 cm = 0.12 m (since 1 cm = 0.01 m)
Angular velocity (ω) = 61.5 rad/s
The moment of inertia (I) for a uniform disk is given by the formula:
I = (1/2) * m * r^2
Using the formula:
L = I * ω
First, calculate the moment of inertia:
I = (1/2) * m * r^2
= (1/2) * 0.175 kg * (0.12 m)^2
Calculate I:
I = 1.26 x 10^-3 kg·m²
Now, substitute the values into the angular momentum formula:
L = I * ω
= 1.26 x 10^-3 kg·m² * 61.5 rad/s
Calculating the result, we find that the angular momentum is 0.07749 kg·m²/s.
Therefore, the linear momentum of the Frisbee is 0.28875 kg·m/s and the angular momentum is 0.07749 kg·m²/s.